Question 1

What is the domain of the sine and cosine functions?

Accepted Answer

$$(-\infty, \infty)$$

Question 2

What is the range of the function $$y = \cos x$$?

Accepted Answer

$$[-1, 1]$$

Question 3

Which of the following best describes the period of $$y = \sin x$$?

Accepted Answer

$$2\pi$$

Question 4

For which values of $$x is$$ $$\sin x = 0$$?

Accepted Answer

$$x = n\pi$$,\ n \in \mathbb{Z}$

Question 5

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

Accepted Answer

It is an even function and symmetric about the y-axis.

Question 6

Given $$y = a \sin bx$$, what is the formula for the period?

Accepted Answer

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

Question 7

What is the amplitude of the function $$y = -2 \cos x$$?

Accepted Answer

$$2$$

Question 8

What is the phase shift of $$y = \sin(x - \frac{\pi}{2})$$?

Accepted Answer

$$\frac{\pi}{2}$$ units to the right

Question 9

If $$y = 4 \sin(\frac{1}{2}x)$$, what is the period of the function?

Accepted Answer

$$4\pi$$

Question 10

Which of the following is the correct pattern for the $$y-$$values of $$y = a \cos(bx) at $$the five key points?

Accepted Answer

{$$a, 0, -a, 0, a$$}

Question 11

A sinusoidal function has amplitude 3, period $$\pi$$, and passes through $$(\frac{\pi}{2}, 0)$$, $$(\frac{3\pi}{4}, 3)$$, and $$(\pi, 0). $$Which equation matches the graph?

Accepted Answer

$$y = 3 \sin(2x - \frac{\pi}{2})$$

Question 12

What is the step size between the five key points when graphing $$y = a \sin bx$$?

Accepted Answer

$$\frac{1}{4} of $$the period

Question 13

Which transformation occurs when the equation $$y = 3 \cos(3x + \pi) + 2 is $$graphed compared to $$y = \cos x$$?

Accepted Answer

Vertical stretch by 3, period $$\frac{2\pi}{3}$$, up 2 units, left $$\frac{\pi}{3}$$ units

Question 14

Which of the following is true about the function $$y = \sin(-2x + \frac{\pi}{3})$$?

Accepted Answer

Amplitude is 1, period is $$\pi$$, phase shift is $$\frac{\pi}{6}$$ units left

Question 15

Which of the following best describes the symmetry of $$y = \sin x$$?

Accepted Answer

Odd function, symmetric about the origin

Question 16

If $$y = a \sin(bx - c)$$, how do you find the phase shift?

Accepted Answer

Set $$bx - c = 0$$ and solve for $$x$$

Question 17

Which of the following is the correct range for $$y = a \sin bx$$?

Accepted Answer

$$[-a, a]$$

Question 18

A Ferris wheel makes one complete revolution every 60 seconds. If the height $$h (in $$meters) above the ground is modeled by $$h(t) = 10 \sin(\frac{\pi}{30} t) + 12$$, what is the amplitude and period of the function?

Accepted Answer

Amplitude: 10, Period: $$60$$

Precalculus Study Guide: Sine and Cosine Functions, Domain, Range, Periodicity, and Graphing

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