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Conversion of Radians and Degrees Degree Radian 180 by multiply Radians Degrees 180 by multiply xample 1 Converting from Degrees to Radians [A] 60° [B] 30° xample 2 Converting from Radians to Degrees [A] [B] 4 7 3 5

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Page 1: Conversion of Radians and Degrees Degree Radian Radians Degrees Example 1Converting from Degrees to Radians [A] 60° [B] 30° Example 2Converting from Radians

Conversion of Radians and Degrees

Degree Radian

180by multiply

Radians Degrees

180by multiply

Example 1 Converting from Degrees to Radians

[A] 60° [B] 30°

Example 2 Converting from Radians to Degrees

[A] [B]4

7

3

5

Page 2: Conversion of Radians and Degrees Degree Radian Radians Degrees Example 1Converting from Degrees to Radians [A] 60° [B] 30° Example 2Converting from Radians

Unit CirclesDegrees Radians

Radian Degrees

MemorizeMemorize

π2

π

2π

4π

6π

3π

2

3π

Page 3: Conversion of Radians and Degrees Degree Radian Radians Degrees Example 1Converting from Degrees to Radians [A] 60° [B] 30° Example 2Converting from Radians

Unit Circle (degrees)

30

6090120

150

180

210

240270 300

330

3600

Page 4: Conversion of Radians and Degrees Degree Radian Radians Degrees Example 1Converting from Degrees to Radians [A] 60° [B] 30° Example 2Converting from Radians

Page 5: Conversion of Radians and Degrees Degree Radian Radians Degrees Example 1Converting from Degrees to Radians [A] 60° [B] 30° Example 2Converting from Radians

Lesson 13.6 Circular Functions

Unit Circle Ordered Pair: )sin ,(cos

Example 1 Unit Circle Points (Find Sine & Cosine)

A]

31

,3

32P B]

43

,47

P

31

sin

332

cos

43

sin

47

cos

Page 6: Conversion of Radians and Degrees Degree Radian Radians Degrees Example 1Converting from Degrees to Radians [A] 60° [B] 30° Example 2Converting from Radians

Example 2 Exact Values Using Trig Ration (Calculator Free)

A] 675cos B]

65

sin

30º

-1 2

3

21

Page 7: Conversion of Radians and Degrees Degree Radian Radians Degrees Example 1Converting from Degrees to Radians [A] 60° [B] 30° Example 2Converting from Radians

Page 8: Conversion of Radians and Degrees Degree Radian Radians Degrees Example 1Converting from Degrees to Radians [A] 60° [B] 30° Example 2Converting from Radians

Page 9: Conversion of Radians and Degrees Degree Radian Radians Degrees Example 1Converting from Degrees to Radians [A] 60° [B] 30° Example 2Converting from Radians

Page 10: Conversion of Radians and Degrees Degree Radian Radians Degrees Example 1Converting from Degrees to Radians [A] 60° [B] 30° Example 2Converting from Radians

Unit Circle with Common Measures

Page 11: Conversion of Radians and Degrees Degree Radian Radians Degrees Example 1Converting from Degrees to Radians [A] 60° [B] 30° Example 2Converting from Radians

)225sin(

1.

Page 12: Conversion of Radians and Degrees Degree Radian Radians Degrees Example 1Converting from Degrees to Radians [A] 60° [B] 30° Example 2Converting from Radians

π32

cos

4.

Page 13: Conversion of Radians and Degrees Degree Radian Radians Degrees Example 1Converting from Degrees to Radians [A] 60° [B] 30° Example 2Converting from Radians

π

611

tan

7.

Page 14: Conversion of Radians and Degrees Degree Radian Radians Degrees Example 1Converting from Degrees to Radians [A] 60° [B] 30° Example 2Converting from Radians

π34

cot

10.

Page 15: Conversion of Radians and Degrees Degree Radian Radians Degrees Example 1Converting from Degrees to Radians [A] 60° [B] 30° Example 2Converting from Radians

π

34

cos

11.

Page 16: Conversion of Radians and Degrees Degree Radian Radians Degrees Example 1Converting from Degrees to Radians [A] 60° [B] 30° Example 2Converting from Radians

13. Name the given trigRatios at the ordered Pair (-5, 12)

Sin θ =

Cot θ =

Page 17: Conversion of Radians and Degrees Degree Radian Radians Degrees Example 1Converting from Degrees to Radians [A] 60° [B] 30° Example 2Converting from Radians

16. Name the given trigRatios at the ordered Pair (-5, 0)

Sin θ =

Cot θ =

Page 18: Conversion of Radians and Degrees Degree Radian Radians Degrees Example 1Converting from Degrees to Radians [A] 60° [B] 30° Example 2Converting from Radians

2

cosπ

19.

Page 19: Conversion of Radians and Degrees Degree Radian Radians Degrees Example 1Converting from Degrees to Radians [A] 60° [B] 30° Example 2Converting from Radians

Example 1: Evaluate Trig Functions Given a Point

a) (5, –12) b) (–3, 4)

sin θ = csc θ =

cos θ = sec θ =

tan θ = cot θ =

sin θ = csc θ =

cos θ = sec θ =

tan θ = cot θ =

-3

4 5θ

5

4

4

5

5

3

3

5

3

4

4

3

Page 20: Conversion of Radians and Degrees Degree Radian Radians Degrees Example 1Converting from Degrees to Radians [A] 60° [B] 30° Example 2Converting from Radians

Example 2: Quadrant Angles

a) 270° b) 2π

sin θ = csc θ =

cos θ = sec θ =

tan θ = cot θ =

sin θ = csc θ =

cos θ = sec θ =

tan θ = cot θ =

0 UND

1 1

0 UND

Page 21: Conversion of Radians and Degrees Degree Radian Radians Degrees Example 1Converting from Degrees to Radians [A] 60° [B] 30° Example 2Converting from Radians

45˚

Calculator Free Trigonometry

[1]10

45sinx

[2]x

1245cos

[3] Jim is standing 40 feet from the base of a flagpole. He is looking a the top of the pole with and angle of elevation of 45˚. Find the height of the flagpole.

Page 22: Conversion of Radians and Degrees Degree Radian Radians Degrees Example 1Converting from Degrees to Radians [A] 60° [B] 30° Example 2Converting from Radians

Calculator Free Trigonometry

60˚

30˚

[1]10

60sinx

[2]x

1230tan

[3] A 20 foot ramp has an angle of elevation of 30˚. Find the vertical rise of the ramp.

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