Q: If $$\csc$$^{-1}$$(x) = \theta$$, which of the following is true?

$$\sin(\theta) = \dfrac{1}{x}$$

Q: Which of the following is the correct range for the inverse secant function $$y = \sec$$^{-1}$$(x)$$?

$$[0, \pi],\ y \neq \dfrac{\pi}{2}$$

Question 1

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

Accepted Answer

$$(-\infty, -1] \cup [1, \infty)$$

Question 2

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

Accepted Answer

$$\dfrac{\pi}{3}$$

Question 3

If $$\csc$$^{-1}$$(x) = 	heta$$, which of the following is true?

Accepted Answer

$$\sin(	heta) = \dfrac{1}{x}$$

Question 4

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

Accepted Answer

$$\dfrac{\pi}{4}$$

Question 5

Evaluate $$\csc$$^{-1}$$(-2)$$ and select the correct answer.

Accepted Answer

$$-\dfrac{\pi}{6}$$

Question 6

Which of the following expressions is equivalent to $$	an(\sin$$^{-1}$$(\dfrac{3}{5}))$$?

Accepted Answer

$$\dfrac{3}{4}$$

Question 7

Suppose $$	heta = \cot$$^{-1}$$(\dfrac{1}{5})$$ with $$0 \u003c 	heta \u003c \pi. $$What is $$\sin(	heta)$$?

Accepted Answer

$$\dfrac{5}{\sqrt{26}}$$

Question 8

Find the exact value of $$\cos(	an$$^{-1}$$(\dfrac{4}{3})).$$

Accepted Answer

$$\dfrac{3}{5}$$

Question 9

If $$	heta = \csc$$^{-1}$$(2\sqrt{2})$$, what is $$\cos(	heta)$$?

Accepted Answer

$$\dfrac{\sqrt{2}}{4}$$

Question 10

Which of the following is the range of the inverse cotangent function $$y = \cot$$^{-1}$$(x)$$?

Accepted Answer

$$(0, \pi)$$

Question 11

A ladder leans against a wall making an angle $$	heta$$ with the ground such that $$\sec(	heta) = 1.25. $$What is $$	heta in $$radians (rounded to two decimal places)?

Accepted Answer

$$0.80$$

Question 12

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

Accepted Answer

$$\sqrt{1-u^2$}$$

Question 13

If $$	heta = \cot$$^{-1}$$(-\dfrac{1}{2})$$ and $$0 \u003c 	heta \u003c \pi$$, what is $$\sin(	heta)$$?

Accepted Answer

$$\dfrac{2}{\sqrt{5}}$$

Question 14

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

Accepted Answer

$$\dfrac{1}{\sqrt{8}}$$

Question 15

If $$	heta = \sec$$^{-1}$$(-2)$$, what is $$\cos(	heta)$$?

Accepted Answer

$$-\dfrac{1}{2}$$

Question 16

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

Accepted Answer

$$[0, \pi],\ y 
eq \dfrac{\pi}{2}$$

Question 17

Evaluate $$\cos(\sin$$^{-1}$$(\dfrac{4}{5})).$$

Accepted Answer

$$\dfrac{3}{5}$$

Question 18

If $$	heta = \csc$$^{-1}$$(-\sqrt{2})$$, what is $$\sin(	heta)$$?

Accepted Answer

$$-\dfrac{1}{\sqrt{2}}$$

Question 19

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

Accepted Answer

$$\dfrac{1}{\sqrt{5}}$$

Question 20

Suppose $$	heta = \cot$$^{-1}$$(\dfrac{3}{4}). $$What is $$\cos(	heta)$$?

Accepted Answer

$$\dfrac{3}{5}$$

Analytic Trigonometry: Inverse Trigonometric Functions (Secant, Cosecant, Cotangent)

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