College Math Placement Test Trigonometry 2 — Questions and Answers
Question 1: What is the exact value of tan(135°)?
- -1 (Correct answer)
- 1
- √2
- -√2
Correct answer: -1
tan(135°) = tan(180° - 45°) = -tan(45°) = -1.
Question 2: Which identity is equivalent to sin²θ + cos²θ?
- 1 (Correct answer)
- 0
- tan²θ
- sec²θ
Correct answer: 1
The Pythagorean identity states sin²θ + cos²θ = 1 for all angles θ.
Question 3: Convert 5π/6 radians to degrees.
- 150° (Correct answer)
- 120°
- 210°
- 300°
Correct answer: 150°
Multiply by 180/π: (5π/6) × (180/π) = 900/6 = 150°.
Question 4: A right triangle has legs of length 5 and 12. What is sin of the angle opposite the leg of length 5?
- 5/13 (Correct answer)
- 12/13
- 5/12
- 12/5
Correct answer: 5/13
The hypotenuse is √(25+144)=13, so sin = opposite/hypotenuse = 5/13.
Question 5: What is the period of y = sin(2x)?
- π (Correct answer)
- 2π
- π/2
- 4π
Correct answer: π
The period of y = sin(bx) is 2π/b, so period = 2π/2 = π.
Question 6: Which of the following equals cos(−θ)?
- cos θ (Correct answer)
- −cos θ
- sin θ
- −sin θ
Correct answer: cos θ
Cosine is an even function, so cos(−θ) = cos θ.
Question 7: If sin θ = 3/5 and θ is in Quadrant II, what is cos θ?
- -4/5 (Correct answer)
- 4/5
- -3/4
- 3/4
Correct answer: -4/5
cos²θ = 1 − 9/25 = 16/25, so cos θ = ±4/5; cosine is negative in QII, so −4/5.
College Math Placement Test Trigonometry 2
What is the exact value of tan(135°)?