Pre-Calculus Name ____________________ Review – Unit 5 Find the exact values of the following. If the answer is an angle, state the angle in RADIANS. (NO CALCULATOR) 1. tan(cos-1 1) = _____ 2. cos(tan-1 1) = _____ 3. cos(csc-1 (-2)) = _____

4. tan(sin-1 ½ ) = _____ 5. cos-1 (cos ) = _____ 6. sin(sin-1 2) = _____

7. cos-1(cos 0) = _____ 8. tan-1 ( ) = _____ 9. cot-1 ( ) = _____ Use your general knowledge of trig and IDENTITIES to solve the following (NO CALCULATOR). 10. sec 20° sin 70° = _____ 11. Given sin α = and .

a) cos = _____ b) tan α = _____

12. Simplify: csc(-x)sin(-x) 13. Simplify: tan sin + cos Find the exact values of the following (NO CALCULATOR). 14. cos(sin-1 (-2/7) = _____ 15. sin(tan-1 ¾) = _____ 16. cos(sin-1 2/x ) = _____ Prove the following identities (NO CALCULATOR): 17. sin x + cos x cot x = csc x 18. sec x – cos x = sinx tan x 19. (1 + sin )2 = 2(1 + sin ) – cos2 20. cos4 x – sin4 x = cos2 x – sin2 x 21. 22. tan x (sin x + cot x cos x ) = sec x

Answerkey

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25. An object moves in simple harmonic motion described by the equation , where t is measured in seconds and d in centimeters. Find the following:

A) the maximum displacement

B) the frequency

C) the time required to complete one cycle

26. An object is attached to a coiled spring. The object is initially at its rest position. After that, it is pulled down and then released. Write an equation for the distance of the object from it rest position after t seconds given the following information.

Distance from rest position at t = 0 is 0 Amplitude is ¼ inch Period is 5 seconds.

27. An object in simple harmonic motion has a frequency of ¼ oscillation per minute and an amplitude of 8 feet. Write an equation in the form d = a sin ωt for the object’s simple harmonic motion.

28. A person seated on a Ferris Wheel of a radius of 100ft makes one rotation every 30 seconds. The center of the wheel is 105ft above the ground. Find and graph a function to represent a person’s height above the ground at any time of a 2-min ride. Assume uniform speed from the beginning to the end of the ride and that a person is at the level of the center of the wheel and headed up when the ride begins.

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31. 32.

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33. 34.

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c. Find the limit as x approaches 0. c. Find the limit as x approaches -1+.

d. Is there anywhere the limit DNE? d. Find the limit as x approaches 2.

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35.

Type: ______________________________

Domain: _____________________________

Range: ______________________________

x-int: ______________________________

y-int: ______________________________

max: ______________________________

min: ______________________________

trans: ______________________________

inc/dec: _____________________________

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For the following questions point P is on the terminal side of angle 6. Evaluate the six trig functions for 6.

37. (-3, 6) 38. (12, 7)

39. ( -5, -3) 40. (4, 9)

41. Use a right triangle to determine the values of all trigonometric functions of 6, where cos 6 = 5/7

42. Find csc 6 and cot 6 if tan 6 = -4/3 and sin 6 > 0

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