Question 1

Which of the following statements correctly describes the period of the function $$y = \sin(Bx)$$?

Accepted Answer

$$\frac{2\pi}{B}$$

Question 2

What is the amplitude of the function $$y = A \cos(x)$$?

Accepted Answer

$$A$$

Question 3

Which property is true for the sine function $$y = \sin(x)$$?

Accepted Answer

It is an odd function.

Question 4

If the graph of $$y = \cos(x) is $$shifted vertically upward by 3 units, what is the new equation?

Accepted Answer

$$y = \cos(x) + 3$$

Question 5

For the function $$y = \sin(x)$$, which of the following points is a relative minimum?

Accepted Answer

$$(\frac{3\pi}{2}, -1)$$

Question 6

What is the range of the function $$y = 4 \sin(x)$$?

Accepted Answer

$$[-4, 4]$$

Question 7

Which of the following is the y-intercept of the function $$y = \cos(x)$$?

Accepted Answer

$$(0, 1)$$

Question 8

A function $$y = \sin(Bx)$$ completes one cycle from $$x = 0 to$$ $$x = \frac{\pi}{2}. $$What is the value of $$B$$?

Accepted Answer

$$4$$

Question 9

Which of the following points is NOT a quarter point for one cycle of $$y = \sin(x)$$?

Accepted Answer

$$(\frac{\pi}{4}, 1)$$

Question 10

If $$y = \cos(Bx)$$ has a period of $$\frac{\pi}{3}$$, what is the value of $$B$$?

Accepted Answer

$$6$$

Question 11

Which of the following describes the symmetry of the cosine function $$y = \cos(x)$$?

Accepted Answer

It is symmetric about the y-axis.

Question 12

Given the function $$y = 2 \sin(3x)$$, what is the amplitude and period?

Accepted Answer

Amplitude: $$2$$, Period: $$\frac{2\pi}{3}$$

Question 13

Which equation represents a sine function with amplitude 5 and period $$\pi$$?

Accepted Answer

$$y = 5 \sin(2x)$$

Question 14

If the graph of $$y = \sin(x) is $$reflected across the x-axis, what is the new equation?

Accepted Answer

$$y = -\sin(x)$$

Question 15

Which of the following is a zero of the function $$y = \cos(x)$$?

Accepted Answer

$$x = \frac{\pi}{2}$$

Question 16

A medical device uses the function $$y = 3 \cos(4x) to $$model oscillations. What is the maximum value the device can reach?

Accepted Answer

$$3$$

Question 17

Which of the following is true about the domain of $$y = \sin(x)$$ and $$y = \cos(x)$$?

Accepted Answer

Both have domain $$(-\infty, \infty).$$

Question 18

If $$y = \sin(x) is $$transformed to $$y = 2 \sin(x)$$, what happens to the graph?

Accepted Answer

The amplitude doubles.

Question 19

Which of the following points is a maximum for $$y = \cos(x)$$?

Accepted Answer

$$(0, 1)$$

Question 20

A sound wave is modeled by $$y = 0.5 \sin(6x). $$What is the period of the wave?

Accepted Answer

$$\frac{2\pi}{6}$$

The Graphs of Sine and Cosine Functions

Study Guide - Practice Questions