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13.3.1 Convert angle measures between degrees and radians. PowerPoint PPT Presentation


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B. D. Warm-Up Label all angles that are multiples of 30 o , 45 o , 60 o , and 90 o around the origin. Learning Goals. 13.3.1 Convert angle measures between degrees and radians. 13.3.2Find the values of trigonometric functions on the unit circle.

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13.3.1 Convert angle measures between degrees and radians.

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13 3 1 convert angle measures between degrees and radians

B.

D.

Warm-Up

Label all angles that are multiples of 30o, 45o, 60o, and 90o around the origin.

Learning Goals

13.3.1 Convert angle measures between degrees and radians.

13.3.2Find the values of trigonometric functions on the unit circle.

13.3.3 Learn strategies to quickly recall the angles (in degrees and radians) as well as the trig. values for sin, cos, and tan of the unit circle.

You have measured angles in degrees; today you will learn to measure angles on another scale called _____________.

Example 1: Converting Between Degrees and Radians

Convert each measure from degrees to radians or from radians to degrees.

A. – 60°

C. 80°


13 3 1 convert angle measures between degrees and radians

THE UNIT CIRCLE

What are the following exact values?

sin(45)=sin(30)=sin(60)=

cos(45)=cos(30)=cos(60)=

tan(45)=tan(30)=tan(60)=


13 3 1 convert angle measures between degrees and radians

B.

tan

Example 2: Using the Unit Circle to Evaluate Trig Functions

Use the unit circle to find the exact value of each trigonometric function.

A.

cos 225°

C.

sin 315°

D.

tan 180°

E.

Example 3: Using Reference Angles to Evaluate Trig Functions

A. Use a reference angle to find the exact value of the sine, cosine, and tangent of 330°.


13 3 1 convert angle measures between degrees and radians

Use a reference angle to find the exact value of the sine, cosine, and tangent of the angles listed below.

A. 270°

B.11π

6

C. -30°


13 3 1 convert angle measures between degrees and radians

Example 4: Automobile Application

A. A tire of a car makes 653 complete rotations in 1 min. The diameter of the tire is 0.65 m. To the nearest meter, how far does the car travel in 1 s?

Step 1 Find the radius of the tire.

Step 2 Find the angle θthrough which the tire rotates in 1 second.

Step 3 Find the length of the arc intercepted by radians.


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