$$|x| \geq 1$$ and $$0 \leq y \leq \pi$$, $$y \neq \frac{\pi}{2}$$

$$0 \leq y \leq \pi$$, $$y \neq \frac{\pi}{2}$$

Question 1

Which of the following is the correct domain and range for the inverse secant function $$y = \sec$$^{-1}$$ x$$?

Accepted Answer

$$|x| \geq 1$$ and $$0 \leq y \leq \pi$$, $$y 
eq \frac{\pi}{2}$$

Question 2

Find the exact value of $$\csc$$^{-1}$$(2).$$

Accepted Answer

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

Question 3

Evaluate $$\cos\left(\sin$$^{-1}$$\left(-\frac{1}{2}\right)\right).$$

Accepted Answer

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

Question 4

If $$\cot 	heta = \frac{1}{5}$$ and $$0 \u003c 	heta \u003c \pi$$, what is $$\sin 	heta$$?

Accepted Answer

Question 5

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

Accepted Answer

$$\frac{1}{\sqrt{10}}$$

Question 6

Which of the following is the correct definition for $$y = \cot$$^{-1}$$ x$$?

Accepted Answer

$$y = \cot$$^{-1}$$ x if $$and only if $$x = \cot y$$, $$0 \u003c y \u003c \pi$$

Question 7

Write $$\cos(\cot$$^{-1}$$ u) as an $$algebraic expression in terms of $$u.$$

Accepted Answer

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

Question 8

A ladder leans against a wall making an angle $$	heta$$ with the ground such that $$\sec 	heta = 2. $$What is $$	heta$$?

Accepted Answer

Question 9

Evaluate $$	an\left(\cos$$^{-1}$$\left(-\frac{1}{3}ight)ight).$$

Accepted Answer

$$-2\sqrt{2}$$

Question 10

Which of the following is NOT in the range of $$y = \csc$$^{-1}$$ x$$?

Accepted Answer

$$y = 0$$

Question 11

If $$	heta = \cot$$^{-1}$$\left(-\frac{1}{2}ight)$$, what is the value of $$\sin 	heta$$?

Accepted Answer

$$\frac{2}{\sqrt{5}}$$

Question 12

A medical imaging device uses the angle $$	heta$$ such that $$\sec 	heta = -1. $$What is $$	heta in $$the principal range?

Accepted Answer

$$\pi$$

Question 13

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

Accepted Answer

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

Question 14

Which of the following statements is true about the range of $$y = \sec$$^{-1}$$ x$$?

Accepted Answer

$$0 \leq y \leq \pi$$, $$y 
eq \frac{\pi}{2}$$

Question 15

If $$	heta = \cos$$^{-1}$$\left(-\frac{1}{3}ight)$$, what is $$\sin 	heta$$?

Accepted Answer

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

Question 16

A satellite dish is installed so that $$\csc 	heta = -2. $$What is $$	heta in $$the principal range?

Accepted Answer

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

Analytic Trigonometry: Inverse Secant, Cosecant, and Cotangent Functions

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