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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. - PowerPoint PPT Presentation
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13-3 The Unit Circle
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.
Learning Goals
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° B.
C. 80° D.
Warm-Up
Label all angles that are
multiples of 30o, 45o, 60o,
and 90o around the origin.
13-3 The Unit CircleTHE UNIT CIRCLEWhat 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 The Unit Circle
Example 2: Using the Unit Circle to Evaluate Trig Functions
Use the unit circle to find the exact value of each trigonometric function.
cos 225°A. tan B.
sin 315° tan 180°C.
E.
D.
QII
Sin θ
Cos θ
Tan θ
QI
Sin θ
Cos θ
Tan θ
QIII
Sin θ
Cos θ
Tan θ
QIV
Sin θ
Cos θ
Tan θ
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 The Unit Circle
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 The Unit Circle
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 θ through which the tire rotates in 1 second.
Step 3 Find the length of the arc intercepted by radians.