Quiz

1) Sketch an angle of and then find its reference angle

7

3

2) Find the supplementary angle to 5

7

3) Find the arccos( ) in both radians and degrees.

3

2

4) Find the arcsin(.3279) in both radians and degrees.

Quiz

1) Sketch an angle of and then find its reference angle

x

y

Since it is 180º half way around the reference angle is 180 – 125 = 55º

7

3

7/3 = 2.3333 which means that it goes all the way around and ends up in he first quadrant

7

3

Quiz

2) Find the supplementary angle to

5

7x

5

7

5

7

2

7x

5

7

Quiz

3) Find the arccos( ) in both radians and degrees.

3

2

4) Find the arcsin(.3279) in both radians and degrees.

arccos( ) = 3

230 radiansor

Because the cos(30) = and the cos( ) =

3

23

26

arcsin(.3279) = 19.14 .3341 radiansor

Because the sin of either one = .3279 if you are in the right mode

Law of Sines - Radians

Nothing changes when the angles are shown in radians – you just need to make certain your calculator is in radian mode

The law of sines is still the same

A

C

B

a

bc

sin sin sin

a b c

A B C

Law of Sines

A

C

B

a

b = 32ft

c

sin sin sin

a b c

A B C

Find side c

C =

32

sin sin5 4

c

B =

Now we cross multiply – make sure the calculator is in radian mode when taking the sin

32*sin *sin4 5

c

32*.7071 *.5878c22.6272 .5878c.5878 .5878

38.49 ft c

5

Law of Sines

A

C

B

b = 23ft

c

sin sin sin

a b c

A B C

Find angle B14 23

sinsin7

B

A =

Now we cross multiply 23*sin 14*sin

7B

23*.4339 14*sin B9.9797 14*sin B

14 14sin .7128B

a = 14ftNow we simply do 2nd sin (.7128) to get the angle

1sin (.7128) .7935 radians

7

We can find the area of any triangle using two of the sides and the sine of the angle that is between the two sides

Make sure the angle is between the two sides

A

C

B

a

bc

Area of Any Triangle Using Sines

Angle A is between b and c, Angle B is between a and c, Angle C is between a and b

The formula is easy to use – just be sure that your calculator is in the proper mode

A

C

B

a

bc

Area of Any Triangle Using Sines

1sin

2Area ab C

1sin

2Area bc A

1sin

2Area ac B

In general its ½(two of the sides)(sin of the angle between them)

Area of Any Triangle Using Sines

A

C

B

b = 23ft

c

Find the area

C =

a = 14ft

7

1sin

2Area ab C

1(23)(14)sin

2 7Area

1(23)(14)(.4339)

2Area

269.86Area ft

Area of Any Triangle Using Sines

A

C

B

b = 34ft

c = 18ft

Find the area

A =

a

38

1sin

2Area bc A

1(34)(18)sin 38

2Area

1(34)(18)(.6157)

2Area

2188.40Area ft