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Unit 2 of 5

Unit 2: Trigonometry

Study guide for CLEP CLEP Precalculus — Unit 2: Trigonometry. Practice questions, key concepts, and exam tips.

51

Practice Questions

13

Flashcards

4

Key Topics

Key Concepts to Study

Unit circle and radian measure
Trigonometric functions and identities
Law of sines and law of cosines
Inverse trigonometric functions

Sample Practice Questions

Try these 5 questions from this unit. Sign up for full access to all 51.

Q1MEDIUM

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?

A) 15 seconds
B) 30 seconds
C) 45 seconds
D) 60 seconds
E) 20 seconds
Show Answer

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.

Q2MEDIUM

Find the period of y = 3sin(2x).

A) π
B) 2π
C) π/2
D) 3π
E) 4π
Show Answer

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).

Q3EASY

Consider the function f(x) = 2sin(3x + π) + 1. Which of the following represents a vertical shift of the function?

A) f(x) = 2sin(3x + π) - 2
B) f(x) = 2sin(3x + π) + 3
C) f(x) = sin(3x + π) + 1
D) f(x) = 2sin(3x) + 1
E) f(x) = 2sin(3x + π) + 1.5
Show Answer

Answer: B — A vertical shift occurs when a constant is added to or subtracted from the function.

Q4HARD

Solve $sec^{2}$(θ) - 1 = 0 for θ.

A) θ = 0, π/2
B) θ = π/4, 3π/4
C) θ = 0, π
D) θ = π/2, 3π/2
E) θ = π/3, 2π/3
Show Answer

Answer: C — θ = 0, π is correct because $sec^{2}$(θ) - 1 = 0 => $tan^{2}$(θ) = 0 => θ = 0, π.

Q5MEDIUM

Solve the equation 2sin(x) = 1 for x in the interval [0, 2π).

A) π/6, 5π/6
B) π/4, 3π/4
C) π/3, 2π/3
D) π/12, 5π/12
E) π/2, 3π/2
Show Answer

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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Study Tips for Unit 2: Trigonometry

  • Focus on understanding concepts, not memorizing facts — CLEP tests application
  • Practice with timed questions to build exam-day speed
  • Review explanations for wrong answers — they reveal common misconceptions
  • Use flashcards for key terms, practice questions for deeper understanding

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