AP Precalculus Trigonometric Functions

Question 1

What is the period of f(x) = 4 sin(πx/3) + 2?

Accepted Answer

6

Answer

For f(x) = a sin(bx) + d, the period is 2π/|b|. Here b = π/3, so the period is 2π ÷ (π/3) = 6.

Question 2

For g(x) = −2 cos(x) + 5, which pair gives the midline and the amplitude?

Accepted Answer

Midline y = 5, amplitude 2

Answer

The midline is y = d = 5. The amplitude is |a| = |−2| = 2, so the graph oscillates between 3 and 7.

Question 3

Which set contains all solutions of 2 sin x = √3 on the interval [0, 2π)?

Accepted Answer

x = π/3 and x = 2π/3

Answer

Dividing by 2 gives sin x = √3/2. Sine equals √3/2 at the reference angle π/3 in Quadrant I and at π − π/3 = 2π/3 in Quadrant II.

Question 4

What is the value of arcsin(sin(5π/6))?

Accepted Answer

π/6

Answer

sin(5π/6) = 1/2, and arcsin returns the angle in [−π/2, π/2] whose sine is 1/2, which is π/6.

Question 5

What is the range of y = sec x?

Accepted Answer

(−∞, −1] ∪ [1, ∞)

Answer

Since sec x = 1/cos x and |cos x| ≤ 1 (with cos x ≠ 0), |sec x| ≥ 1. The range is therefore (−∞, −1] ∪ [1, ∞).

AP Precalculus Practice Test