Question 1

Given the function $$y = \sin(x - \frac{\pi}{2})$$, what is the phase shift and in which direction does the graph move?

Accepted Answer

Phase shift of $$\frac{\pi}{2}$$ units to the right

Question 2

For the function $$y = \cos(2x + \frac{\pi}{2})$$, what is the phase shift?

Accepted Answer

Phase shift of $$\frac{\pi}{4}$$ units to the left

Question 3

Which of the following best describes the effect of the phase shift in the function $$y = \sin(x + \frac{\pi}{3})$$?

Accepted Answer

The graph shifts $$\frac{\pi}{3}$$ units to the left

Question 4

A sound wave is modeled by $$y = 3\cos(4x - \pi). $$What is the phase shift of this wave?

Accepted Answer

Phase shift of $$\frac{\pi}{4}$$ units to the right

Question 5

If $$y = \sin(2x - \pi)$$ models the position of a pendulum, what is the phase shift?

Accepted Answer

Phase shift of $$\frac{\pi}{2}$$ units to the right

Question 6

Which equation represents a cosine function shifted $$\frac{\pi}{6}$$ units to the right?

Accepted Answer

$$y = \cos(x - \frac{\pi}{6})$$

Question 7

A Ferris wheel's height is modeled by $$y = 10\sin(\frac{\pi}{4}x + \frac{\pi}{2}). $$What is the phase shift?

Accepted Answer

Phase shift of $$-2$$ units (2 units to the left)

Question 8

Given $$y = \sin(3x + \pi)$$, what is the phase shift and direction?

Accepted Answer

Phase shift of $$\frac{\pi}{3}$$ units to the left

Question 9

Which of the following functions has a phase shift of $$\frac{\pi}{2}$$ units to the left?

Accepted Answer

$$y = \sin(x + \frac{\pi}{2})$$

Question 10

A temperature cycle is modeled by $$y = 5\cos(2x - \frac{\pi}{3}). $$What is the phase shift?

Accepted Answer

Phase shift of $$\frac{\pi}{6}$$ units to the right

Question 11

If $$y = \sin(x - c)$$, what is the general rule for the direction of the phase shift?

Accepted Answer

The graph shifts $$c$$ units to the right

Question 12

Which of the following best describes the phase shift for $$y = \cos(4x + 2)$$?

Accepted Answer

Phase shift of $$\frac{1}{2}$$ units to the left

Question 13

A daylight cycle is modeled by $$y = 2\sin(\frac{\pi}{6}x - \frac{\pi}{3}). $$What is the phase shift?

Accepted Answer

Phase shift of $$\frac{2}{1}$$ units to the right

Question 14

Which transformation occurs to the graph of $$y = \sin x to $$obtain $$y = \sin(x + \frac{\pi}{4})$$?

Accepted Answer

Shift $$\frac{\pi}{4}$$ units to the left

Question 15

Given $$y = \cos(5x - 10)$$, what is the phase shift?

Accepted Answer

Phase shift of $$2$$ units to the right

Question 16

If $$y = \sin(2x + \pi)$$, what is the phase shift and direction?

Accepted Answer

Phase shift of $$\frac{\pi}{2}$$ units to the left

Phase Shifts of Sine and Cosine Functions

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