Unit 2 of 5
Study guide for CLEP CLEP Precalculus — Unit 2: Trigonometry. Practice questions, key concepts, and exam tips.
46
Practice Questions
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Flashcards
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Key Topics
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A Ferris wheel has a diameter of 60 feet and is rotating at a constant rate. The height of a seat on the wheel above the ground can be modeled by a periodic function H, where H(t) = 30sin(πt/15) + 40. What is the period of this function?
15 seconds
30 seconds
45 seconds
60 seconds
20 seconds
Answer: B — The period of the function H(t) = 30sin(πt/15) + 40 is given by T = 2π / |B|, where B is the coefficient of t. So, T = 2π / (π/15) = 30 seconds.
Find the period of y = 3sin(2x).
π
2π
π/2
3π
4π
Answer: A — π is correct because period of sin(bx) is 2π/|b|, so for sin(2x), it's π, not B which is for sin(x).
Consider the function f(x) = 2sin(3x + π) + 1. Which of the following represents a vertical shift of the function?
f(x) = 2sin(3x + π) - 2
f(x) = 2sin(3x + π) + 3
f(x) = sin(3x + π) + 1
f(x) = 2sin(3x) + 1
f(x) = 2sin(3x + π) + 1.5
Answer: B — A vertical shift occurs when a constant is added to or subtracted from the function.
Solve (θ) - 1 = 0 for θ.
θ = 0, π/2
θ = π/4, 3π/4
θ = 0, π
θ = π/2, 3π/2
θ = π/3, 2π/3
Answer: C — θ = 0, π is correct because $sec^{2}$(θ) - 1 = 0 => $tan^{2}$(θ) = 0 => θ = 0, π.
Solve the equation 2sin(x) = 1 for x in the interval [0, 2π).
π/6, 5π/6
π/4, 3π/4
π/3, 2π/3
π/12, 5π/12
π/2, 3π/2
Answer: A — To solve 2sin(x) = 1, first divide both sides by 2 to get sin(x) = 1/2. Recall that sin(π/6) = 1/2 and sin(5π/6) = 1/2. These angles are in the first and second quadrants respectively where sine is positive, thus the solutions in the interval [0, 2π) are x = π/6 and x = 5π/6.
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