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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Label all angles that are multiples of 30o, 45o, 60o, and 90o around the origin.
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°
What are the following exact values?
sin(45)= sin(30)= sin(60)=
cos(45)= cos(30)= cos(60)=
tan(45)= tan(30)= tan(60)=
Example 2: Using the Unit Circle to Evaluate Trig Functions
Use the unit circle to find the exact value of each trigonometric function.
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°.
Use a reference angle to find the exact value of the sine, cosine, and tangent of the angles listed below.
Example 4: Automobile Application cosine, and tangent of the angles listed below.
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.