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 $$y = \cos\left(2x\right)$$?

Accepted Answer

$$\pi$$

Question 3

Which of the following points is a quarter point on the graph of $$y = \sin(x) in $$the interval $$[0, 2\pi]$$?

Accepted Answer

$$\left(\frac{\pi}{2}, 1\right)$$

Question 4

The function $$y = \cos(x) is $$classified as which type of function?

Accepted Answer

Even

Question 5

What is the range of the function $$y = 4 \sin(x)$$?

Accepted Answer

$$[-4, 4]$$

Question 6

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

Accepted Answer

$$3$$

Question 7

Which of the following statements is true about the graph of $$y = \sin(x)$$?

Accepted Answer

It is symmetric about the origin.

Question 8

A sound wave can be modeled by $$y = 2 \cos(5x). $$What is the amplitude and period of this wave?

Accepted Answer

Amplitude: $$2$$, Period: $$\frac{2\pi}{5}$$

Question 9

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

Accepted Answer

The y-intercept is $$0.$$

Question 10

If $$y = A \sin(Bx)$$ has a maximum value of $$5$$ and a minimum value of $$-5$$, what is the value of $$A$$?

Accepted Answer

$$5$$

Question 11

A Ferris wheel rotates such that the height $$h (in $$meters) above the ground at time $$t (in $$minutes) is given by $$h = 10 + 8 \sin\left(\frac{\pi}{5} t\right). $$What is the period of the Ferris wheel's rotation?

Accepted Answer

$$10$$ minutes

Question 12

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

Accepted Answer

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

Question 13

Which property distinguishes the sine function from the cosine function?

Accepted Answer

The sine function is odd, while the cosine function is even.

Question 14

If $$y = 2 \sin\left(\frac{x}{3}\right)$$, what is the period of the function?

Accepted Answer

$$6\pi$$

Question 15

A medical device uses a signal modeled by $$y = 0.5 \cos(4x). $$What is the range of this function?

Accepted Answer

$$[-0.5, 0.5]$$

Question 16

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

Accepted Answer

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

Question 17

If the graph of $$y = \sin(x) is $$shifted up by $$2$$ units, what is the new range?

Accepted Answer

$$[1, 3]$$

Question 18

Which of the following best describes the zeros of $$y = \sin(x)$$?

Accepted Answer

$$x = n\pi$$ where $$n is an $$integer

Question 19

A chemical reaction oscillates according to $$y = 6 \sin(2x). $$What is the distance between the maximum and minimum values of this function?

Accepted Answer

$$12$$

Question 20

Which of the following is NOT a step in sketching the graph of $$y = A \sin(Bx)$$?

Accepted Answer

Divide the interval $$[0, 2\pi]$$ into three equal subintervals.

Graphs and Properties of Sine and Cosine Functions

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