Pre-Calculus



Pre-CalculusName ________________________________Review – Unit 5Find the exact values of the following. If the answer is an angle, state the angle in RADIANS. (NO CALCULATOR) tan(cos-1 1) = _____2. cos(tan-1 1) = _____3. cos(csc-1 (-2)) = _____4. tan(sin-1 ? ) = _____5. cos-1 (cos 7π4 ) = _____6. sin(sin-1 2) = _____7. cos-1(cos 0) = _____8. tan-1 (-3) = _____9. cot-1 (-3) = _____Use your general knowledge of trig and IDENTITIES to solve the following (NO CALCULATOR).10. sec 20° sin 70° = _____11. Given sin α = -23 and 3π2≤α≤2π . (Hint use co-functions) a) cos π2-α= _____b) tan α = _____12. Simplify: csc(-x)sin(-x) 13. Simplify: tanθsinθ + cosθFind the exact values of the following (NO CALCULATOR).14. cos(sin-1 (-27) = _____15. sin(tan-1 34) = _____16. cos(sin-1 2x ) = _____Prove the following identities (NO CALCULATOR):17. sin x + cos x cot x = csc x18. sec x – cos x = sinx tan x19. (1 + sin θ)2 = 2(1 + sin θ) – cos2 θ20. cos4 x – sin4 x = cos2 x – sin2 x21. 1+tanθ+cscθsecθ=sinθ+cosθ+cotθ 22. tan x (sin x + cot x cos x ) = sec xGraph the following trig functions (NO CALCULATOR):-95252813050023. y=3csc(θ3+π2)-124. fx= -2tan(θ-π3)3590925114300025. 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 displacementB) the frequencyC) the time required to complete one cycle26. 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 0Amplitude is ? inchPeriod is 5 seconds.27. An object in simple harmonic motion has a frequency of ? 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. CUMULATIVE REVIEW: Solve the following limits algebraically. HINT: Factor, Cancel, Plug in 29. 30. 31. 32. Graph the piece-wise function. Answer any questions following. 33. 34. a. Find f(x) when x = 4.a. Find g(x) when x = -1.b. Find the limit as x approaches -1.b. Find the limit as x approaches -1.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.Use the given functions to find the following: 35. Type: ______________________________Domain: _____________________________Range: ______________________________x-int:______________________________y-int: ______________________________max:______________________________min:______________________________trans:______________________________inc/dec:_____________________________36. Type: ______________________________Domain: _____________________________Range: ______________________________x-int:______________________________y-int: ______________________________max:______________________________min:______________________________trans:______________________________inc/dec:______________________________For the following questions point P is on the terminal side of angle θ. Evaluate the six trig functions for θ. 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 θ, where cos θ = 5/7 42. Find csc θ and cot θ if tan θ = -4/3 and sin θ > 0 ................
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