University:
North Central College
Course:
MATH 140 | Precalculus
Academic year:

2019
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361

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6
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Honors Pre-Calculus Review Chapter 4 Test In #1-21, find the exact value without the use of a calculator. 1. sin(330°) = -1/2 2. cot(120°) = -√3/3 3. sec(135°) = -√2 4. sin(-780°) = -√3/2 5. tan(-7π/4) = 1 6. csc(5π/6) = 2 7. cos(13π/3) = 1/2 8. csc(arctan(2.5)) = √(29)/5 9. tan(arctan(35)) = 35 (35 is in domain for arctan) 10. sin(arcsin(-1.1)) = No Solution, -1.1 is outside domain for sin⁻¹ 11. arccos(cos(7π/2)) = π/2 12. sin⁻¹(sin(7π/4)) = -π/4 13. cos⁻¹(cos(4π/3)) = 2π/3 14. cos(arctan(-1)) = √2/2 15. arcsin(sin(6π/7)) = π/7 16. tan⁻¹(√3/3) = π/6 17. sin(arccos(-1/2)) = √3/2 18. arccos(cos(0)) = 0 19. sec(arcsin(3/5)) = 5/4 20. csc(arctan(-12/5)) = -13/12 21. sec(tan⁻¹(-1.5)) = √13/2 Write an algebraic expression that is equivalent to the expression. 22. tan(arccos(x/2)) = √(4-x²) / x 23. sec(arcsin(x-1)) = 1 / √(-x² + 2x) 24. Find the exact values of the six trigonometric functions of θ = 5π/6 sinθ = -1/2 cosθ = -√3/2 tanθ = √3/3 cscθ = -2 secθ = -2√3/3 cotθ = √3 25. Simplify the following: a. (sec²θ - 1)(csc²θ - 1) = 1 b. (tan²θ)/(secθ + 1) + 1 = secθ c. (sinθ - cosθ)/(1 - cos²θ) = cotθ Graph the following: 26a. y = 2cos(π/2)(x-1) a = 2, amp = 2 b = π/2, period = 2π/b = 4 c = 1, phase shift = 1 to the right 26b. y = -2cos2x a = -2, amp = 2, vert. stretch of 2 w/ reflection b = 2, period = π c = 0 26c. y = -3sin4π(x+1) a = -3, amp = 3, w/ reflection b = 4π, period = π/2 c = -1, phase shift = 1 to the left 26d. y = (1/2)sec2(x-π/2) a = 1/2, vert. shrink of 1/2 b = 2, period = π c = π/2, phase shift to the right 26a. y = 2cos(π/2)(x-1) Amplitude: 2 Period: 2π / (π/2) = 4 Phase shift: 1 unit to the right Key points: (1, 2), (2, 0), (3, -2), (4, 0), (5, 2) 26b. y = -2csc2θ Amplitude: 2, vertical reflection Period: 2π / 2 = π Key points: (π/4, -2), (π/2, undefined), (3π/4, 2), (π, undefined), (5π/4, -2) 26c. y = -3sin4π(x+1) Amplitude: 3, vertical reflection Period: 2π / 4π = 1/2 Phase shift: 1 unit to the left Key points: (-1, 0), (-7/8, -3), (-3/4, 0), (-1/8, 3), (1/4, 0) 26d. y = (1/2)sec2(x-π/2) Amplitude: 1/2, vertical shrink Period: 2π / 2 = π Phase shift: π/2 units to the right Key points: (π/4, 1/2), (π/2, undefined), (3π/4, -1/2), (π, undefined), (5π/4, 1/2)

Math Chapter 4 Test Review Solution

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