trigonometric ratios of special angles

8/10/2019 Trigonometric Ratios of Special Angles

1/28


2/28

Trigonometric Ratios ofQuadrantal Angles

90

270

How do we find trig values in this case?

90

180

270

360

90

180

270

360


3/28

Recall:

y

x

y

x

r

P(x, y)

Let P(x, y) be a pointon the terminal sideof angle .

sin = yr cos = x

r tan = y

x

csc =r

y

sec =r

x

cot =x

y


4/28

Consider a unit circle

sin 90=

= 1

cos 90=x

r= 0

tan 90= yx

=


5/28


sin 180=

= 0

cos 180=x

r= 1

tan 180= yx

= 0


6/28


sin 270=

= 1

cos 270=x

r= 0

tan 270= yx

=


7/28


sin 360=

= 0

cos 360=x

r= 1

tan 360= yx

= 0


8/28

Summary


9/28

Consider an equilateral triangle.

Divide the triangle into 2 equal right angledtriangles.

60

60

60

22

2


10/28

60

60

30

1

22

2

Consider just one ofthe triangles.

60

30

1

2


11/28

1

2

3

60sin

2

3

60cos

60tan

2

13

30sin

30cos

30tan

2

3

2

1

3

1

312 22

60

30


12/28

1

1

45

45

211

22

2

45cos45sin

45tan2

11

Let the equal sides have

length 1.


13/28

Trigonometric Ratio of

Special Angles


14/28

Unit Circle

30

1

2

3

2

1

3

2,1

2
http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971


15/28

Unit Circle

45

2

2

2

2

1

2

2,

2

2


16/28

Unit Circle

601

2

3

2

1

1

2,

3

2


17/28

Unit Circle1

2

,3

2

3

2,1

2

2

2,

2

2

sin 30 =1

2

cos 30 =3

2

tan 30 =3

3

csc 30 = 2

sec 30 =2 3

3

cot 30 = 3
http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971


18/28

Unit Circle1

2

,3

2

3

2,1

2

2

2,

2

2

sin 45 =2

2

cos 45 =2

2

tan 45 = 1

csc 45 = 2

sec 45 = 2

cot 45 = 1
http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971


19/28

Unit Circle1

2

,3

2

3

2,1

2

2

2,

2

2

sin 60 =3

2

cos 60 =1

2

tan 60 = 3

csc 60 =2 3

3

sec 60 = 2

cot 60 =3

3
http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971


20/28

In general,

sin = cos =

tan =

csc =1

sec =

1

cot =
http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971


21/28

Unit Circle 0,1

1,0

0,1

1,0 sin 90 = 1

cos 90 = 0

tan 90 =

csc 90 = 1

sec 90 =

cot 90 = 0
http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971


22/28

Unit Circle 0,1

sin 180 = 0

cos 180 = 1

tan 180 = 0

1,0

0,1

1,0

csc 180 =

sec 180 = 1

cot 180 =
http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971


23/28

Unit Circle 0,1

1,0

0,1

1,0 sin 270 = 1

cos 270 = 0

tan 270

= csc 270 = 1

sec 270 =

cot 270 = 0
http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971


24/28

Unit Circle 0,1

sin 360 = 0

cos 360 = 1

tan 360 = 0

1,0

0,1

1,0

csc 360 =

sec 360 = 1

cot 360 =
http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971http://www.google.com.ph/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gESzgTwe6azndM&tbnid=yPyMIl7vGZsCqM:&ved=0CAcQjRw&url=http://imgarcade.com/1/blank-unit-circle/&ei=3JA6VP7QBMqfugTesYD4AQ&bvm=bv.77161500,d.c2E&psig=AFQjCNFSpYWxmnqBocF-B2pYQLZK_YUiQA&ust=1413210639698971


25/28

Degrees

0

30

45

60

90

120

135

150

180

210

245

270300

315

345

360


26/28

Example 1: Find sin 225

Get the quadrant:

III -> Cast rule -> sine is (-)Get the reference angle :

45

sin 45= 2/2

sin 225= -2/2

Determining the trig ratio from thespecial triangles or fingers


27/28

Example 2: Find tan 120

Get the quadrant:

II -> Cast rule ->tangent is (-)

Get the reference angle :

60->Using fingers or special triangles, we

determine tan 60= 3

tan 120=

-3


28/28

Seatwork:

Page 197 (workbook)

trigonometric ratios of special angles

Documents