Question 1

What is the amplitude and period of the function $y = -6 \cos x$?

Accepted Answer

Amplitude: $6$, Period: $2\pi$

Question 2

Given $y = 4 \sin x$, which of the following describes its amplitude and period?

Accepted Answer

Amplitude: $4$, Period: $2\pi$

Question 3

For the function $y = -8 \sin \left( \frac{1}{2} x \right)$, what is the amplitude and period?

Accepted Answer

Amplitude: $8$, Period: $4\pi$

Question 4

What is the amplitude, period, and phase shift of $y = 8 \sin \left( 2x + \pi \right)$?

Accepted Answer

Amplitude: $8$, Period: $\pi$, Phase Shift: $-\frac{\pi}{2}$

Question 5

Given $y = 2 \cos \left( 2x - \pi \right)$, what is the period and phase shift?

Accepted Answer

Period: $\pi$, Phase Shift: $\frac{\pi}{2}$

Question 6

For $y = -8 \sin \left( \frac{1}{3} x + \frac{\pi}{2} \right)$, what is the amplitude and period?

Accepted Answer

Amplitude: $8$, Period: $6\pi$

Question 7

What is the amplitude, period, and phase shift of $y = -4 \sin \left( \frac{1}{2} x + \frac{\pi}{4} \right)$?

Accepted Answer

Amplitude: $4$, Period: $4\pi$, Phase Shift: $-2\pi/4 = -\frac{\pi}{2}$

Question 8

If $y = 4 \cos x + 2$, what is the midline of the function?

Accepted Answer

$y = 2$

Question 9

Which equation represents a sine curve with amplitude $3$, period $\pi$, and phase shift $\frac{\pi}{4}$ to the right?

Accepted Answer

$y = 3 \sin \left( 2x - \frac{\pi}{2} \right)$

Question 10

A sound wave is modeled by $y = 5 \sin \left( 4x \right)$. What is the frequency of the wave?

Accepted Answer

$\frac{2}{\pi}$

Question 11

Which transformation occurs when the graph of $y = \sin x$ is changed to $y = \sin (x - \frac{\pi}{3})$?

Accepted Answer

A phase shift of $\frac{\pi}{3}$ units to the right

Question 12

If $y = 2 \cos (3x)$ models the height of a Ferris wheel seat over time, what is the period of rotation?

Accepted Answer

$\frac{2\pi}{3}$

Question 13

Which of the following is the correct equation for a cosine curve with amplitude $5$, period $2\pi$, and midline $y = -1$?

Accepted Answer

$y = 5 \cos x - 1$

Question 14

A temperature oscillates daily and is modeled by $T = 10 \sin \left( \frac{\pi}{12} t \right) + 70$. What is the maximum temperature?

Accepted Answer

$80$

Question 15

Which equation represents a sine curve with amplitude $2$, period $\frac{2\pi}{5}$, and phase shift $\frac{\pi}{5}$ to the left?

Accepted Answer

$y = 2 \sin \left( 5x + \pi \right)$

Question 16

If $y = 3 \sin (x) + 2$, what is the range of the function?

Accepted Answer

$[-1, 5]$

Question 17

A light intensity varies as $I = 7 \cos \left( \frac{\pi}{6} t \right)$. What is the period of the intensity cycle?

Accepted Answer

$12$

Question 18

Which of the following describes the effect of the negative sign in $y = -4 \sin x$?

Accepted Answer

It reflects the graph across the $x$-axis

Question 19

If $y = 5 \sin (2x - \frac{\pi}{2})$, what is the phase shift?

Accepted Answer

$\frac{\pi}{4}$ units to the right

Graphing and Analyzing Trigonometric Functions: Amplitude, Period, and Phase Shift

Study Guide - Practice Questions