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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