Question 1

Which of the following statements best describes the relationship between a function and its inverse?

Accepted Answer

The graph of the inverse function is a reflection of the original function about the line $$y = x.$$

Question 2

What is the principal value range for the inverse sine function $$y = \arcsin(x)$$?

Accepted Answer

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

Question 3

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

Accepted Answer

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

Question 4

Which of the following is the correct domain for the inverse cosine function $$y = \arccos(x)$$?

Accepted Answer

$$[-1, 1]$$

Question 5

Evaluate $$\arccos\left(-\frac{1}{2}\right).$$

Accepted Answer

$$\frac{2\pi}{3}$$

Question 6

Which of the following is the range of the inverse tangent function $$y = \arctan(x)$$?

Accepted Answer

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

Question 7

Find the exact value of $$\arctan(1).$$

Accepted Answer

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

Question 8

Which of the following is true about the inverse cotangent function $$y = \arccot(x)$$?

Accepted Answer

Its range is $$(0, \pi).$$

Question 9

If $$\sin(	heta) = x$$ for $$-\frac{\pi}{2} \leq 	heta \leq \frac{\pi}{2}$$, what is $$\arcsin(\sin(	heta))$$?

Accepted Answer

$$	heta$$

Question 10

Evaluate $$\sin(\arccos(0.6)).$$

Accepted Answer

$$0.8$$

Question 11

Which of the following expressions is undefined?

Accepted Answer

$$\arccos(2)$$

Question 12

A ladder leans against a wall making an angle $$	heta$$ with the ground. If $$\cos(	heta) = 0.8$$, what is $$	heta$$?

Accepted Answer

$$\arccos(0.8)$$

Question 13

Find the exact value of $$\arccos(1).$$

Accepted Answer

$$0$$

Question 14

If $$	an(	heta) = x$$ for $$-\frac{\pi}{2} \u003c 	heta \u003c \frac{\pi}{2}$$, what is $$\arctan(	an(	heta))$$?

Accepted Answer

$$	heta$$

Question 15

Which of the following best describes how to graph $$y = \arcsin(x)$$?

Accepted Answer

Reflect the graph of $$y = \sin(x) ($$restricted to $$\left[ -\frac{\pi}{2}, \frac{\pi}{2} \right]) $$about the line $$y = x.$$

Question 16

Find the exact value of $$\arctan(\sqrt{3}).$$

Accepted Answer

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

Question 17

Which of the following is the correct domain for the inverse sine function $$y = \arcsin(x)$$?

Accepted Answer

$$[-1, 1]$$

Question 18

If $$	heta = \arcsin\left(\frac{\sqrt{2}}{2}ight)$$, what is $$	heta$$?

Accepted Answer

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

Question 19

A ramp rises at an angle $$	heta$$ such that $$	an(	heta) = 2. $$What is $$	heta$$?

Accepted Answer

$$\arctan(2)$$

Inverse Trigonometric Functions – Study Notes

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