Question 1

What is the amplitude and period of the function $$y = 3 \sin x$$?

Accepted Answer

Amplitude: $$3$$, Period: $$2\pi$$

Question 2

Which of the following equations represents a sine function with amplitude $$2$$ and period $$4\pi$$?

Accepted Answer

$$y = 2 \sin \frac{1}{2}x$$

Question 3

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

Accepted Answer

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

Question 4

Given $$y = 2 \cos x + 1$$, what is the maximum value of $$y$$?

Accepted Answer

$$3$$

Question 5

Which transformation occurs when $$y = \sin x is $$changed to $$y = \sin(x - \frac{\pi}{2})$$?

Accepted Answer

A horizontal shift right by $$\frac{\pi}{2}$$

Question 6

If $$y = -4 \cos \pi x$$, what is the amplitude and period?

Accepted Answer

Amplitude: $$4$$, Period: $$2$$

Question 7

Which of the following best describes the range of $$y = 2 \cos x + 1$$?

Accepted Answer

$$[-1, 3]$$

Question 8

A sound wave can be modeled by $$y = 0.5 \sin(4x). $$What is the period of this wave?

Accepted Answer

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

Question 9

Which equation represents a cosine function with amplitude $$\frac{3}{2}$$, period $$\pi$$, and phase shift $$-\frac{\pi}{2}$$?

Accepted Answer

$$y = \frac{3}{2} \cos(2x + \pi)$$

Question 10

If a Ferris wheel's height above the ground is modeled by $$y = 10 \sin\left(\frac{\pi}{15} t\right) + 12$$, what is the vertical shift and what does it represent?

Accepted Answer

Vertical shift: $$12$$, representing the center height above ground

Question 11

What is the minimum value of $$y = 3 \sin(2x - \frac{\pi}{3})$$?

Accepted Answer

$$-3$$

Question 12

Which of the following statements is true about the graph of $$y = \cos x$$?

Accepted Answer

It is an even function

Question 13

A temperature sensor records data modeled by $$y = 5 \cos(\frac{\pi}{12} t) + 20. $$What is the maximum temperature recorded?

Accepted Answer

$$25$$

Question 14

Which function has a period of $$\frac{2\pi}{3}$$?

Accepted Answer

$$y = \sin 3x$$

Question 15

If $$y = 2 \sin(\frac{1}{2}x)$$, what is the value of $$y$$ when $$x = 2\pi$$?

Accepted Answer

$$0$$

Question 16

Which of the following best describes the effect of increasing $$A in$$ $$y = A \sin x$$?

Accepted Answer

The amplitude increases

Question 17

What is the period of $$y = -4 \cos \pi x$$?

Accepted Answer

$$2$$

Question 18

Which of the following is the correct formula for the period of $$y = A \sin Bx$$?

Accepted Answer

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

Question 19

If $$y = 2 \cos x + 1$$, what is the midline of the graph?

Accepted Answer

$$y = 1$$

Question 20

Which of the following best describes the graph of $$y = \sin x$$?

Accepted Answer

It is periodic with period $$2\pi$$ and range $$[-1, 1]$$

Graphs of Sine and Cosine Functions: Properties, Variations, and Transformations

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