College Math Placement Test Trigonometry 5 — Questions and Answers
Question 1: What is the domain of y = arccos(x)?
- [−1, 1] (Correct answer)
- (−∞, ∞)
- [0, π]
- [−π/2, π/2]
Correct answer: [−1, 1]
arccos is only defined for inputs where cosine is valid, i.e., x ∈ [−1, 1].
Question 2: Simplify: sin θ / cos θ + cos θ / sin θ
- 1/(sin θ cos θ)
- tan θ + cot θ
- 2/(sin 2θ)
- All of the above (Correct answer)
Correct answer: All of the above
sin θ/cos θ + cos θ/sin θ = tan θ + cot θ = (sin²θ + cos²θ)/(sin θ cos θ) = 1/(sin θ cos θ) = 2/sin 2θ.
Question 3: What is the Law of Cosines used to find?
- A side or angle in any triangle (Correct answer)
- Only angles in right triangles
- Only the hypotenuse
- Only area of a triangle
Correct answer: A side or angle in any triangle
The Law of Cosines (c² = a² + b² − 2ab cos C) applies to any triangle to find sides or angles.
Question 4: What is the exact value of sin(7π/6)?
- -1/2 (Correct answer)
- 1/2
- -√3/2
- √3/2
Correct answer: -1/2
7π/6 = 210°; reference angle is 30°, and sine is negative in QIII, so sin = −1/2.
Question 5: The graph of y = cos(x) is shifted 2 units upward. What is the new range?
- [1, 3] (Correct answer)
- [-1, 1]
- [-3, -1]
- [0, 2]
Correct answer: [1, 3]
The original range [−1, 1] shifts up by 2, giving [−1+2, 1+2] = [1, 3].
Question 6: Which value satisfies sin θ = cos θ for 0 ≤ θ < 2π?
- π/4 and 5π/4 (Correct answer)
- π/4 only
- π/2 and 3π/2
- 0 and π
Correct answer: π/4 and 5π/4
sin θ = cos θ ⟹ tan θ = 1, which holds at θ = π/4 and θ = 5π/4 in [0, 2π).
Question 7: What is the area of a triangle with sides a = 6, b = 8, and included angle C = 30°?
- 12 (Correct answer)
- 24
- 6√3
- 48
Correct answer: 12
Area = (1/2)ab sin C = (1/2)(6)(8) sin 30° = 24 × 1/2 = 12.
College Math Placement Test Trigonometry 5
What is the domain of y = arccos(x)?