Question 1

Which of the following best describes the amplitude of the function $y = -3 \sin(2x)$?

Accepted Answer

$3$

Question 2

What is the period of the function $y = \cos\left(\frac{x}{3}\right)$?

Accepted Answer

$6\pi$

Question 3

Given the function $y = 4 \sin(5x)$, what is its range?

Accepted Answer

$[-4, 4]$

Question 4

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

Accepted Answer

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

Question 5

A Ferris wheel rotates such that the height $h$ (in meters) of a passenger above the ground at time $t$ (in seconds) is modeled by $h(t) = 10 + 8\sin\left(\frac{\pi}{15}t\right)$. What is the period of the motion?

Accepted Answer

$30$

Question 6

Which of the following is the correct equation for a cosine function with amplitude $5$ and period $\pi$?

Accepted Answer

$y = 5\cos(2x)$

Question 7

If the graph of $y = \sin(x)$ is shifted vertically upward by $3$ units and stretched by a factor of $2$, what is the new equation?

Accepted Answer

$y = 2\sin(x) + 3$

Question 8

Which of the following points is a $y$-intercept of the function $y = \cos(x)$?

Accepted Answer

$(0, 1)$

Question 9

A sound wave can be modeled by $y = 0.5\sin(440\pi t)$, where $t$ is in seconds. What is the frequency of the wave in Hz?

Accepted Answer

$220$

Question 10

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

Accepted Answer

$-2$

Question 11

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

Accepted Answer

$x = 0$

Question 12

If $y = 3\sin(2x)$, what is the value of $y$ when $x = \frac{\pi}{4}$?

Accepted Answer

$0$

Question 13

Which of the following best describes the symmetry of the sine function?

Accepted Answer

It is odd and symmetric about the origin.

Question 14

A temperature sensor records the temperature $T$ (in $^\circ$C) in a room as $T(t) = 20 + 5\cos\left(\frac{\pi}{12}tight)$, where $t$ is in hours. What is the maximum temperature recorded?

Accepted Answer

$25$

Question 15

Which of the following is the correct period for the function $y = \sin(4x)$?

Accepted Answer

$\frac{2\pi}{4} = \frac{\pi}{2}$

Question 16

Given the function $y = A\sin(Bx)$, if the period is $\pi$ and the amplitude is $2$, what is the equation?

Accepted Answer

$y = 2\sin(2x)$

Question 17

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

Accepted Answer

They occur at $x = (2n+1)\frac{\pi}{2}$, where $n$ is an integer.

Question 18

If $y = \sin(-2x)$, which property of the sine function allows you to rewrite this as $y = -\sin(2x)$?

Accepted Answer

Odd property: $\sin(-x) = -\sin(x)$

Question 19

A graph of a trigonometric function passes through the origin and has a period of $\frac{\pi}{2}$. Which of the following could be its equation?

Accepted Answer

$y = \sin(4x)$

Question 20

If $y = 2\cos(3x)$, what is the value of $y$ when $x = \frac{\pi}{6}$?

Accepted Answer

$1$

Graphs of Sine and Cosine Functions – Precalculus Study Notes

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