College Math Placement Test Trigonometry 5

Question 1

What is the domain of y = arccos(x)?

Accepted Answer

[−1, 1]

Answer

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

Accepted Answer

All of the above

Answer

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?

Accepted Answer

A side or angle in any triangle

Answer

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)?

Accepted Answer

-1/2

Answer

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?

Accepted Answer

[1, 3]

Answer

The original range [−1, 1] shifts up by 2, giving [−1+2, 1+2] = [1, 3].

College Math Placement Test Practice Test