MPT Trigonometry 3

Question 1

What is the amplitude of y = -3cos(x)?

Accepted Answer

3

Answer

Amplitude is the absolute value of the leading coefficient: |-3| = 3.

Question 2

If sin(θ) = -√3/2 and θ is in the third quadrant, what is θ?

Accepted Answer

4π/3

Answer

sin(60°) = √3/2, and in the third quadrant: π + π/3 = 4π/3.

Question 3

Simplify: (1 - cos²θ) / sin(θ) for sin(θ) ≠ 0.

Accepted Answer

sin(θ)

Answer

1 - cos²θ = sin²θ by the Pythagorean identity, so sin²θ/sinθ = sinθ.

Question 4

What is the reference angle for 210°?

Accepted Answer

30°

Answer

210° is in the third quadrant; 210° - 180° = 30° is the reference angle.

Question 5

What is the range of the function y = arcsin(x)?

Accepted Answer

[-π/2, π/2]

Answer

The range of arcsin (inverse sine) is [-π/2, π/2] by definition.

(MPT) UCF Math Placement Test Practice Test