Question 1

Which of the following best describes the amplitude of the function $$y = -3 \sin(x)$$?

Accepted Answer

$$3$$

Question 2

What is the period of the function $$y = \sin(2x)$$?

Accepted Answer

$$\pi$$

Question 3

Which of the following points is a quarter point on one cycle of $$y = \cos(x)$$?

Accepted Answer

$$(\frac{\pi}{2}, 0)$$

Question 4

The range of the function $$y = A \sin(x) is$$:

Accepted Answer

$$[-|A|, |A|]$$

Question 5

If $$y = \cos(Bx)$$ has a period of $$\frac{2\pi}{3}$$, what is the value of $$B$$?

Accepted Answer

$$3$$

Question 6

Which property is true for the sine function $$y = \sin(x)$$?

Accepted Answer

It is an odd function, so $$\sin(-x) = -\sin(x).$$

Question 7

At which $$x-$$value does $$y = \sin(x)$$ reach its minimum in one cycle?

Accepted Answer

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

Question 8

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

Accepted Answer

Amplitude: $$0.5$$, Period: $$\frac{\pi}{2}$$

Question 9

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

Accepted Answer

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

Question 10

If the graph of $$y = A \cos(Bx)$$ passes through the origin, which function form should you use to model it?

Accepted Answer

$$y = A \sin(Bx)$$

Question 11

Which of the following statements is true about the cosine function $$y = \cos(x)$$?

Accepted Answer

It is an even function, so $$\cos(-x) = \cos(x).$$

Question 12

A Ferris wheel rotates such that the height of a passenger above the ground is modeled by $$y = 10 \sin(\frac{\pi}{5}x) + 12. $$What is the period of the rotation?

Accepted Answer

$$10$$

Question 13

Which of the following is NOT a characteristic of the sine function $$y = \sin(x)$$?

Accepted Answer

The y-intercept is $$1.$$

Question 14

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

Accepted Answer

$$[-2, 2]$$

Question 15

Which of the following ordered pairs is a zero of $$y = \sin(x)$$?

Accepted Answer

$$(\pi, 0)$$

Question 16

If $$y = 5 \sin(2x)$$, what is the value of $$x at $$which the function reaches its maximum in one cycle?

Accepted Answer

$$\frac{\pi}{4}$$

Question 17

A medical device uses a signal modeled by $$y = 2 \cos(\frac{\pi}{6}x). $$What is the period of the signal?

Accepted Answer

$$12$$

Question 18

Which step is necessary when sketching $$y = A \sin(Bx) if$$ $$B \u003c 0$$?

Accepted Answer

Rewrite the function using the odd property of sine to ensure $$B \u003e 0.$$

Question 19

Which of the following is the correct set of five quarter points for one cycle of $$y = \sin(x)$$?

Accepted Answer

$$(0, 0), (\frac{\pi}{2}, 1), (\pi, 0), (\frac{3\pi}{2}, -1), (2\pi, 0)$$

Question 20

A city’s temperature over a day is modeled by $$y = 8 \sin(\frac{\pi}{12}x) + 65. $$What is the amplitude and the range of the temperature?

Accepted Answer

Amplitude: $$8$$, Range: $$[57, 73]$$

Graphs and Properties of Sine and Cosine Functions

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