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Mastery Objectives Find values of trigonometric functions for any angle. Find values of trigonometric functions using the unit circle.

quadrantal angle reference angle unit circle periodic function period

Trig Functions of any angle

Let (–4, 3) be a point on the terminal side of an angle θ in standard position. Find the exact values of the six trigonometric functions of θ.

Let (–3, 6) be a point on the terminal side of an angle Ө in standard position. Find the exact values of the six trigonometric functions of Ө. A. B. C. D.

Quadrantal Angles

Find the exact value of cos π. If not defined, write undefined. Answer: –1

Example 3 Find the exact value of tan 450°. If not defined, write undefined. Answer: undefined

Find the exact value of. If not defined, write undefined. Answer: 0

A.–1 B.0 C.1 D.undefined Find the exact value of sec If not defined, write undefined.

Reference Angles (Make a bowtie)

Sketch –150°. Then find its reference angle. Answer: 30°

Answer: Sketch. Then find its reference angle.

Find the reference angle for a 520 o angle. A.20° B.70° C.160° D.200°

Steps to Evaluate Trig Functions

Find the exact value of. Answer:

Find the exact value of tan 150º. Answer:

Find the exact value of. Answer:

A. B. C. D. Find the exact value of cos.

Let, where sin θ > 0. Find the exact values of the remaining five trigonometric functions of θ. Answer:

Let csc θ = –3, tan θ < 0. Find the exact values o the five remaining trigonometric functions of θ. A. B. C. D.

A student programmed a 10-inch long robotic arm to pick up an object at point C and rotate through an angle of 150° in order to release it into a container at point D. Find the position of the object at point D, relative to the pivot point O.

Example 6 Cosine ratio  = 150° and r = 10 cos 150° = –cos 30° Solve for x.

Example 6 Sin ratio θ = 150° and r = 10 sin 150° = sin 30° Solve for y. 5 = y

Example 6 Answer: The exact coordinates of D are. The object is about 8.66 inches to the left of the pivot point and 5 inches above the pivot point.

A 4-foot long minute hand on a clock on a bell tower shows a time of 15 minutes past the hour. What is the new position of the end of the minute hand relative to the pivot point at 5 minutes before the next hour? A.6 feet left and 3.4 feet above the pivot point B.3.4 feet left and 2 feet above the pivot point C.3.4 feet left and 6 feet above the pivot point D.2 feet left and 3.4 feet above the pivot point

Unit Circle

Answer: Find the exact value of. If undefined, write undefined.

Answer: corresponds to the point (x, y) = on the unit circle. Find the exact value of. If undefined, write undefined.

Answer:

Find the exact value of sec 270°. If undefined, write undefined. 270° corresponds to the point (x, y) = (0, –1) on the unit circle. Answer: undefined

A. B. C. D. Find the exact value of tan. If undefined, write undefined.

Periodic Functions

Find the exact value of. Answer:

Find the exact value of sin(–300). on the unit circle. Answer:

Find the exact value of. Answer:

A.1 B.–1 C. D. Find the exact value of cos

Homework: Homework: P 251: 1, 4, 9-16, odd, all, thirds, 72,74

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