$$\sin$$^{-1}$$(-x) = -\sin$$^{-1}$$(x)$$ and $$\tan$$^{-1}$$(-x) = -\tan$$^{-1}$$(x)$$

$$\cot$$^{-1}$$ x = \frac{\pi}{2} - \tan$$^{-1}$$ x$$

Question 1

Which of the following statements is TRUE about the relationship between a function $$f$$ and its inverse $$f^{-1}$$?

Accepted Answer

The graph of $$f^{-1} is a $$reflection of the graph of $$f$$ across the line $$y = x.$$

Question 2

Given $$f(x) = x^3$ - 1$$, what is the formula for $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \sqrt[3]{x + 1}$$

Question 3

Which of the following intervals is the restricted domain for $$y = \sin x so $$that it has an inverse function?

Accepted Answer

$$\left[ -\frac{\pi}{2}, \frac{\pi}{2} \right]$$

Question 4

What is the range of the inverse sine function $$y = \sin$$^{-1}$$ x$$?

Accepted Answer

$$\left[ -\frac{\pi}{2}, \frac{\pi}{2} \right]$$

Question 5

Evaluate $$y = \arcsin\left( -\frac{1}{2} \right).$$

Accepted Answer

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

Question 6

Which of the following is the correct domain for $$y = \arccos x$$?

Accepted Answer

$$[-1, 1]$$

Question 7

Find the exact value: $$	an(\arccos(-\frac{5}{13})).$$

Accepted Answer

$$-\frac{12}{5}$$

Question 8

Which of the following is the range of $$y = \arctan x$$?

Accepted Answer

$$\left( -\frac{\pi}{2}, \frac{\pi}{2} \right)$$

Question 9

If $$y = \arccos\left( \frac{1}{2} \right)$$, what is $$y$$?

Accepted Answer

$$\frac{\pi}{3}$$

Question 10

Which of the following is the correct way to evaluate $$\sec$$^{-1}$$ x$$ using a calculator?

Accepted Answer

$$\sec$$^{-1}$$ x = \cos$$^{-1}$$ \left( \frac{1}{x} \right)$$

Question 11

Find the exact value: $$\sin(\arctan(\frac{3}{2})).$$

Accepted Answer

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

Question 12

Which of the following is the correct range for $$y = \arccsc x$$?

Accepted Answer

$$\left[ -\frac{\pi}{2}, 0 \right) \cup \left( 0, \frac{\pi}{2} \right]$$

Question 13

Evaluate $$\arctan(1) in $$radians.

Accepted Answer

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

Question 14

Which of the following is the correct domain for $$y = \arcsec x$$?

Accepted Answer

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

Question 15

Find the exact value: $$	an(2 \arcsin(\frac{2}{5})).$$

Accepted Answer

$$\frac{4}{3}$$

Question 16

If $$y = \arccos(-1)$$, what is $$y$$?

Accepted Answer

$$\pi$$

Question 17

Which of the following is TRUE about the oddness of the inverse sine and tangent functions?

Accepted Answer

$$\sin$$^{-1}$$(-x) = -\sin$$^{-1}$$(x)$$ and $$	an$$^{-1}$$(-x) = -	an$$^{-1}$$(x)$$

Question 18

Find the degree measure of $$	heta if$$ $$	heta = \arccos\left( \frac{1}{2} ight).$$

Accepted Answer

$$60^{\circ}$$

Question 19

Which of the following is the correct way to evaluate $$\cot$$^{-1}$$ x$$ using a calculator?

Accepted Answer

$$\cot$$^{-1}$$ x = \frac{\pi}{2} - 	an$$^{-1}$$ x$$

Inverse Circular (Trigonometric) Functions: Definitions, Properties, and Applications

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