Question 1

Which of the following best describes the range of the function $$y = rac{1}{2} 	ext{sin}(x)$$?

Accepted Answer

$$[-\frac{1}{2}, \frac{1}{2}]$$

Question 2

What is the period of the function $$y = 	ext{cos}(3x)$$?

Accepted Answer

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

Question 3

Which property is true for the function $$y = 	ext{sin}(x)$$?

Accepted Answer

It is an odd function, symmetric about the origin.

Question 4

At which $$x-$$value does $$y = 	ext{cos}(x)$$ reach its minimum value in the interval $$[0, 2\pi]$$?

Accepted Answer

$$x = \pi$$

Question 5

A sound wave can be modeled by $$y = 3	ext{sin}(2x). $$What is the amplitude and period of this wave?

Accepted Answer

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

Question 6

Which of the following ordered pairs is a quarter point on the graph of $$y = 	ext{sin}(x)$$?

Accepted Answer

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

Question 7

If $$y = A	ext{sin}(Bx)$$ has a period of $$4\pi$$ and amplitude $$5$$, what are the values of $$A$$ and $$B$$?

Accepted Answer

$$A = 5, B = \frac{1}{2}$$

Question 8

Which statement is true about the zeros of $$y = 	ext{cos}(x)$$?

Accepted Answer

They occur at $$x = (2n+1)\frac{\pi}{2}$$ for integer $$n.$$

Question 9

A Ferris wheel rotates such that the height of a seat above the ground is modeled by $$y = 10	ext{cos}(x) + 12. $$What is the maximum height reached by the seat?

Accepted Answer

$$22$$

Question 10

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

Accepted Answer

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

Question 11

If $$y = -2	ext{cos}(x)$$, what is the range of the function?

Accepted Answer

$$[-2, 2]$$

Question 12

Which of the following is a property of the cosine function $$y = 	ext{cos}(x)$$?

Accepted Answer

It is even and symmetric about the $$y-$$axis.

Question 13

A medical device uses the function $$y = 0.8	ext{sin}(4x) to $$model a signal. What is the period of the signal?

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

If the graph of $$y = 	ext{sin}(x) is $$stretched vertically by a factor of $$4$$, what is the new amplitude?

Accepted Answer

$$4$$

Question 16

Which of the following points is NOT a quarter point on the graph of $$y = 	ext{cos}(x) in$$ $$[0, 2\pi]$$?

Accepted Answer

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

Question 17

A chemical reaction oscillates according to $$y = 2	ext{sin}(x). $$What is the maximum value reached by the function?

Accepted Answer

$$2$$

Question 18

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

Accepted Answer

It passes through the origin and has a maximum at $$x = \frac{\pi}{2}$$

Question 19

If $$y = 5	ext{cos}(2x)$$, what is the $$x-$$coordinate of the first zero in $$[0, 2\pi]$$?

Accepted Answer

$$x = \frac{\pi}{2}$$

Question 20

A light intensity varies as $$y = 2	ext{cos}(x). $$What is the minimum value of the intensity?

Accepted Answer

$$-2$$

Graphs and Properties of Sine and Cosine Functions

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