Question 1

What is the amplitude of the function $$y = 3 \sin(2x - \frac{\pi}{2}) + 1$$?

Accepted Answer

$$3$$

Question 2

What is the period of the function $$y = 	an(4x)$$?

Accepted Answer

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

Question 3

Which of the following is the correct phase shift for $$y = \cos(2x - \pi)$$?

Accepted Answer

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

Question 4

The function $$y = \sin(x) is$$:

Accepted Answer

Odd

Question 5

What is the range of the function $$y = 4\sin(x - 2\pi) + 3$$?

Accepted Answer

$$[-1, 1]$$ shifted up by $$3$$, so $$[3-4, 3+4] = [-1, 7]$$

Question 6

Which of the following is the correct equation for the vertical asymptotes of $$y = 	an(2x)$$?

Accepted Answer

$$x = \frac{\pi}{4} + n\frac{\pi}{2}$$, $$n \in \mathbb{Z}$$

Question 7

If $$\sin$$^{-1}$$(x) is $$defined for $$x in $$which interval?

Accepted Answer

$$[-1, 1]$$

Question 8

Given $$y = 2\cos(\frac{1}{2}x)$$, what is the period?

Accepted Answer

$$4\pi$$

Question 9

Which of the following is true about the function $$y = 	an(x)$$?

Accepted Answer

It is an odd function

Question 10

What is the value of $$\sin(\frac{5\pi}{6})$$?

Accepted Answer

$$\frac{1}{2}$$

Question 11

Which of the following is the correct range for $$y = 	an(x)$$?

Accepted Answer

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

Question 12

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

Accepted Answer

$$\frac{\pi}{4} to $$the left

Question 13

Which of the following is the correct value for $$\cos$$^{-1}$$(0)$$?

Accepted Answer

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

Question 14

Which property is true for $$\cos(-x)$$?

Accepted Answer

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

Question 15

What is the exact value of $$	an(\frac{\pi}{4})$$?

Accepted Answer

$$1$$

Question 16

Which of the following is the correct formula for the period of $$y = A\sin(Bx + C) + D$$?

Accepted Answer

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

Question 17

If $$y = 	an(3x)$$, what are the equations of the vertical asymptotes in one period?

Accepted Answer

$$x = -\frac{\pi}{6}$$ and $$x = \frac{\pi}{6}$$

Question 18

Which of the following is the correct value for $$\sin$$^{-1}$$(1)$$?

Accepted Answer

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

Question 19

What is the $$y-$$coordinate of the center point for one period of $$y = 	an(x)$$?

Accepted Answer

$$0$$

Question 20

Which of the following is the correct value for $$\cos(\frac{2\pi}{3})$$?

Accepted Answer

$$-\frac{1}{2}$$

Study Guide: Graphs and Properties of Trigonometric Functions (Precalculus)

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