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 $$T (in$$ $$^\circC) in a $$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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