Question 1

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

Accepted Answer

$$-1 \leq x \leq 1$$, $$-\dfrac{\pi}{2} \leq y \leq \dfrac{\pi}{2}$$

Question 2

Evaluate $$\cos$$^{-1}$$(2)$$, if possible.

Accepted Answer

No solution

Question 3

Find the exact value: $$\sin\left(\cos$$^{-1}$$\left(\dfrac{3}{5}\right)\right).$$

Accepted Answer

$$\dfrac{4}{5}$$

Question 4

Which of the following expressions is equivalent to $$\sec$$^{-1}$$(x)$$ for $$x \geq 1$$?

Accepted Answer

$$\cos$$^{-1}$$\left(\dfrac{1}{x}\right)$$

Question 5

Evaluate $$	an\left(\cos$$^{-1}$$\left(-\dfrac{3}{4}ight)ight).$$

Accepted Answer

$$-\dfrac{\sqrt{7}}{3}$$

Question 6

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

Accepted Answer

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

Question 7

Suppose $$	heta = 	an$$^{-1}$$\left(-\dfrac{1}{3}ight). $$What is $$\csc(	heta)$$?

Accepted Answer

$$-\sqrt{10}$$

Question 8

Evaluate $$\sin$$^{-1}$$(1.2)$$, if possible.

Accepted Answer

No solution

Question 9

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

Accepted Answer

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

Question 10

If $$x = \sin(\sin$$^{-1}$$(0.8))$$, what is $$x$$?

Accepted Answer

$$0.8$$

Question 11

Find the exact value: $$\cos\left(\sin$$^{-1}$$\left(-\dfrac{1}{6}\right)\right).$$

Accepted Answer

$$\dfrac{\sqrt{35}}{6}$$

Question 12

Which of the following is the correct range for $$y = 	an$$^{-1}$$ x$$?

Accepted Answer

$$-\dfrac{\pi}{2} \u003c y \u003c \dfrac{\pi}{2}$$

Question 13

Find the exact value: $$	an\left(\sin$$^{-1}$$\left(\dfrac{5}{13}ight)ight).$$

Accepted Answer

$$\dfrac{5}{12}$$

Question 14

Evaluate $$\sin\left(	an$$^{-1}$$\left(\dfrac{4}{3}ight)ight).$$

Accepted Answer

$$\dfrac{4}{5}$$

Question 15

Suppose $$	heta = \cos$$^{-1}$$\left(-\dfrac{3}{5}ight). $$What is $$	an(	heta)$$?

Accepted Answer

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

Question 16

Find the exact value: $$\cos\left(	an$$^{-1}$$(u)ight)$$, where $$u \u003e 0.$$

Accepted Answer

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

Question 17

A ladder leans against a wall making an angle $$	heta$$ with the ground. If $$\cos(	heta) = 0.7$$, what is $$	heta in $$radians (rounded to two decimal places)?

Accepted Answer

$$0.80$$

Question 18

Find the exact value: $$\sin\left(	an$$^{-1}$$\left(-\dfrac{1}{2}ight)ight).$$

Accepted Answer

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

Question 19

If $$x = \cos(\cos$$^{-1}$$(x))$$, what is the restriction on $$x$$ for this equation to hold?

Accepted Answer

$$-1 \leq x \leq 1$$

Inverse Trigonometric Functions: Definitions, Properties, and Applications unit 4.7

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