Question 1

Which of the following best describes the amplitude of the function $$y = -4 \sin(x)$$?

Accepted Answer

$$4$$

Question 2

Given the function $$y = 3 \cos(2x)$$, what is the period of the function?

Accepted Answer

$$\pi$$

Question 3

A Ferris wheel has a maximum height of 50 meters and a minimum height of 10 meters. If its height above the ground can be modeled by a cosine function, what is the amplitude of the function?

Accepted Answer

$$30$$

Question 4

Which transformation occurs when the function $$y = \sin(x) is $$changed to $$y = \sin(2x)$$?

Accepted Answer

Horizontal shrink by a factor of 2

Question 5

What is the phase shift of the function $$y = \cos(3x - \frac{\pi}{2})$$?

Accepted Answer

$$\frac{\pi}{6}$$ units to the right

Question 6

If $$y = 2 + 5 \sin(x)$$ models the height (in meters) of a tide above sea level, what is the midline of the graph?

Accepted Answer

$$y = 2$$

Question 7

Which property distinguishes the sine function from the cosine function?

Accepted Answer

Sine is odd, cosine is even

Question 8

A sound wave can be modeled by $$y = 0.8 \sin(440\pi t). $$What is the period of this wave?

Accepted Answer

$$\frac{1}{440}$$ seconds

Question 9

Given $$y = -3 \cos(x)$$, which statement is true about its graph compared to $$y = 3 \cos(x)$$?

Accepted Answer

It is reflected about the x-axis

Question 10

The function $$y = 2 \sin\left(\frac{x}{2}\right)$$ has which of the following properties?

Accepted Answer

Amplitude 2, period $$4\pi$$

Question 11

A water depth at a dock is modeled by $$y = 5.6 \cos(0.524t - 2.094) + 5.7. $$What is the average water depth?

Accepted Answer

$$5.7$$ feet

Question 12

If the period of $$y = a \sin(bx) is$$ $$\frac{2\pi}{3}$$, what is the value of $$b$$?

Accepted Answer

$$3$$

Question 13

Which equation represents a sine function with amplitude 4, period $$\pi$$, and midline $$y = -2$$?

Accepted Answer

$$y = 4 \sin(2x) - 2$$

Question 14

A skateboarder’s vertical position is modeled by $$y = 1.5 \cos(\pi t) + 2. $$What is the maximum height reached?

Accepted Answer

$$3.5$$ meters

Question 15

Which of the following describes the effect of the transformation $$y = \sin(x) \rightarrow y = \sin(x) + 3$$?

Accepted Answer

Vertical shift up by 3 units

Question 16

If $$y = 2 \cos(3x - \frac{\pi}{2})$$, what is the phase shift?

Accepted Answer

$$\frac{\pi}{6}$$ units to the right

Question 17

A water slide’s height above ground is modeled by $$y = 8 \sin(\frac{\pi}{6} t) + 10. $$What is the minimum height?

Accepted Answer

$$2$$ meters

Question 18

Which of the following is the correct range for $$y = -2 \sin(x)$$?

Accepted Answer

$$[-2, 2]$$

Question 19

If $$y = 3 \sin(2x - \pi)$$, what is the period and phase shift?

Accepted Answer

Period $$\pi$$, phase shift $$\frac{\pi}{2}$$ units right

Question 20

A camera on a rotating platform completes one revolution every 8 seconds. If its horizontal position is modeled by $$y = 5 \cos\left(\frac{\pi}{4} t\right)$$, what is the period?

Accepted Answer

$$8$$ seconds

Graphs of Sine and Cosine Functions: Amplitude, Period, and Transformations

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