Q: What is the domain of the function $$y = \csc x$$?

All $$x$$ such that $$x \neq n\pi$$, where $$n is $$any integer

Q: What is the domain of the function $$y = \frac{1}{\sin x}$$?

All $$x$$ such that $$x \neq n\pi$$, where $$n is $$any integer

Question 1

What is the domain of the function $$y = \csc x$$?

Accepted Answer

All $$x$$ such that $$x 
eq n\pi$$, where $$n is $$any integer

Question 2

What is the period of the secant function $$y = \sec x$$?

Accepted Answer

$$2\pi$$

Question 3

What is the domain of the function $$y = \frac{1}{\sin x}$$?

Accepted Answer

All $$x$$ such that $$x 
eq n\pi$$, where $$n is $$any integer

Question 4

Which of the following statements about $$y = \cot x is $$correct?

Accepted Answer

It has no y-intercepts

Question 5

Given $$y = \cos\left(\frac{1}{6}x + \frac{\pi}{6}\right)$$, what is the amplitude, period, and phase shift?

Accepted Answer

Amplitude: $$1$$, Period: $$2\pi$$, Phase shift: $$-\frac{\pi}{6}$$

Question 6

For $$y = 2\sin\left(\frac{\pi}{3}x - 3\pi\right)$$, what is the amplitude, period, and phase shift?

Accepted Answer

Amplitude: $$2$$, Period: $$6\pi$$, Phase shift: $$3\pi$$

Question 7

Find the exact value of $$\sin$$^{-1}$$\left(\frac{1}{2}\right).$$

Accepted Answer

$$\frac{\pi}{6}$$

Question 8

Find the exact value of $$\cos$$^{-1}$$\left(-\frac{1}{2}\right).$$

Accepted Answer

$$\frac{5\pi}{6}$$

Question 9

Find the exact value of $$	an$$^{-1}$$(1).$$

Accepted Answer

$$\frac{\pi}{4}$$

Question 10

Use your calculator to find $$\sin$$^{-1}$$(-0.7) to $$two decimal places.

Accepted Answer

$$-0.78$$

Question 11

Find $$\sin\left(\sin$$^{-1}$$\left(\frac{5\pi}{6}\right)\right). $$What is the answer?

Accepted Answer

$$\frac{5\pi}{6}$$

Question 12

Find the exact value of $$\sin\left(	an$$^{-1}$$\left(\frac{3}{2}ight)ight).$$

Accepted Answer

$$\frac{3}{\sqrt{13}}$$

Question 13

Find the exact value of $$\cot\left(\sin$$^{-1}$$\left(\frac{1}{2}\right)\right).$$

Accepted Answer

$$\sqrt{3}$$

Question 14

Find the exact value of $$\sin\left(\cos$$^{-1}$$\left(-\frac{1}{3}\right)\right).$$

Accepted Answer

$$\frac{2\sqrt{2}}{3}$$

Question 15

Let $$	heta = \cos$$^{-1}$$\left(-\frac{1}{3}ight). $$What quadrant is $$	heta in$$?

Accepted Answer

Quadrant II

Question 16

Write $$\cos\left(	an$$^{-1}$$ uight) as an $$algebraic expression in terms of $$u$$ for $$u \u003e 0.$$

Accepted Answer

$$\frac{1}{\sqrt{1 + u^2$}}$$

Question 17

Which of the following best describes the shape of $$y = \csc x$$ for $$x$$ between $$0$$ and $$2\pi$$?

Accepted Answer

It consists of two branches with vertical asymptotes at $$x = 0, \pi, 2\pi$$

Question 18

A medical device uses the function $$y = \sin\left(\frac{\pi}{3}x\right) to $$model a periodic signal. If the device records one full cycle in $$6$$ seconds, what is the period of the function in terms of $$x$$?

Accepted Answer

$$6$$

Question 19

A sound wave is modeled by $$y = 2\cos\left(\frac{1}{4}x\right). $$What is the amplitude and period of the wave?

Accepted Answer

Amplitude: $$2$$, Period: $$8\pi$$

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