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 property is true for the cosine function?

Accepted Answer

$$\cos(-x) = \cos(x)$$

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 step size for the key points when graphing $$y = a \sin bx$$?

Accepted Answer

$$\frac{1}{4} \left( \frac{2\pi}{b} \right)$$

Question 9

Which transformation occurs when the equation $$y = \sin(x - \frac{\pi}{2}) is $$graphed?

Accepted Answer

A horizontal shift of $$\frac{\pi}{2}$$ units to the right

Question 10

Given the function $$y = 4 \sin \left( \frac{1}{2} x \right)$$, what is its period?

Accepted Answer

$$4\pi$$

Question 11

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 12

If $$y = 3 \sin(2x - \frac{\pi}{2})$$, what is the phase shift?

Accepted Answer

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

Question 13

Which of the following best describes the graph of $$y = 3 \cos(3x + \pi) + 2$$?

Accepted Answer

Amplitude 3, period $$\frac{2\pi}{3}$$, vertical shift up 2

Question 14

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

Accepted Answer

It is reflected over the y-axis and has a phase shift of $$\frac{\pi}{6} to $$the right

Question 15

Which of the following equations matches the sinusoidal graph with key points $$\left( \frac{\pi}{2}, 0 \right)$$, $$\left( \frac{3\pi}{4}, 3 \right)$$, $$\left( \pi, 0 \right)$$, $$\left( \frac{5\pi}{4}, -3 \right)$$, and $$\left( \frac{3\pi}{2}, 0 \right)$$?

Accepted Answer

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 an odd function?

Accepted Answer

$$y = \sin x$$

Question 18

A sound wave can be modeled by $$y = 2 \sin(4x). $$What is the period of this wave?

Accepted Answer

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

Question 19

If the period of $$y = a \sin bx is$$ $$\pi$$, what is the value of $$b$$?

Accepted Answer

$$2$$

Precalculus Study Guide: Sine and Cosine Functions – Domain, Range, Period, Amplitude, and Graphing

Study Guide - Practice Questions

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