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

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