Precalculus Sine and Cosine Function Values on Unit Circle

Which of the following best describes the rate of change of g over the interval 3π/2 < θ < 2π?

• The rate of change of g is positive and increasing.

• The rate of change of g is positive and decreasing.

• The rate of change of g is negative and increasing.

• The rate of change of g is negative and decreasing.

The function f is given by f(x) = 1 - 2 cos(x). Which of the following is the graph of f for 0 ≤ x ≤ 4π?

• Graph A

• Graph B

• Graph C

• Graph D

The figure shows the graph of a sinusoidal function f. Which of the following values is the period of f?

• 1

• 3

• π

• 2π

The figure shows the graph of a sinusoidal function g. What is the amplitude of g?

• 1

• 2

• 3

• 4

The figure shows the graph of a sinusoidal function f. What are the values of the period and amplitude of f?

• The period is π, and the amplitude is 1.

• The period is π, and the amplitude is 2.

• The period is π/2, and the amplitude is 1.

• The period is π/2, and the amplitude is 2.

The figure shows the graph of a sinusoidal function g. What are the values of the period and amplitude of g?

• The period is 2, and the amplitude is 2.

• The period is 2, and the amplitude is 4.

• The period is 4, and the amplitude is 2.

• The period is 4, and the amplitude is 4.

Which of the following best describes the behavior of g over the interval π/2 < θ < π?

• g is positive and increasing.

• g is positive and decreasing.

• g is negative and increasing.

• g is negative and decreasing.

On the interval [π, 3π/2], which of the following is true about h?

• h is positive and increasing.

• h is positive and decreasing.

• h is negative and increasing.

• h is negative and decreasing.

On the interval [3π/2, 2π], which of the following is true about h?

• h is positive and increasing.

• h is positive and decreasing.

• h is negative and increasing.

• h is negative and decreasing.

Which of the following correctly describes how the rate of change of h is changing on the interval [3π/2, 2π]?

• The rate of change of h is increasing because the graph of h is concave up.

• The rate of change of h is decreasing because the graph of h is concave up.

• The rate of change of h is increasing because the graph of h is concave down.

• The rate of change of h is decreasing because the graph of h is concave down.