Question 1

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

Accepted Answer

$$y is $$the unique angle in $$[-\frac{\pi}{2}, \frac{\pi}{2}]$$ such that $$\sin y = x$$

Question 2

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

Accepted Answer

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

Question 3

Solve for $$x in$$ $$\sin x = \frac{1}{2}$$, where $$0 \leq x \u003c 2\pi.$$

Accepted Answer

$$x = \frac{\pi}{6}, \frac{5\pi}{6}$$

Question 4

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

Accepted Answer

$$[-1, 1]$$

Question 5

If $$	an 	heta = 3$$ and $$	heta is in $$quadrant III, what is $$\sin 	heta$$?

Accepted Answer

$$-\frac{3}{\sqrt{10}}$$

Question 6

Which equation expresses the Pythagorean identity for sine and cosine?

Accepted Answer

$$\sin^2$ x + \cos^2$ x = 1$$

Question 7

Find all solutions to $$2\cos^2$ x - 1 = 0$$ for $$0 \leq x \u003c 2\pi.$$

Accepted Answer

$$x = \frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4}$$

Question 8

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

Accepted Answer

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

Question 9

If $$\sin 	heta = -\frac{1}{2}$$ and $$	heta is in $$quadrant IV, what is $$	heta$$?

Accepted Answer

$$\frac{11\pi}{6}$$

Question 10

Which of the following is the correct formula for $$	an(\arccos x)$$?

Accepted Answer

$$\frac{\sqrt{1-x^2$}}{x}$$

Question 11

Solve for $$x$$: $$\sin(2x) = 0.5$$ for $$0 \leq x \u003c 2\pi.$$

Accepted Answer

$$x = \frac{\pi}{12}, \frac{5\pi}{12}, \frac{13\pi}{12}, \frac{17\pi}{12}$$

Question 12

Which of the following is the correct expression for $$\arctan(1)$$?

Accepted Answer

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

Question 13

If $$\cos x = 0.6$$, what is $$x in $$radians (principal value)?

Accepted Answer

$$x = \arccos(0.6)$$

Question 14

Which of the following is the correct solution for $$	an x = -1 in$$ $$[0, 2\pi)$$?

Accepted Answer

$$x = \frac{3\pi}{4}, \frac{7\pi}{4}$$

Question 15

Which of the following is the correct formula for $$\sin(\arccos x)$$?

Accepted Answer

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

Question 16

If $$\sin x = 0.8$$ and $$x is in $$quadrant II, what is $$x$$?

Accepted Answer

$$x = \pi - \arcsin(0.8)$$

Question 17

Which of the following is the correct solution for $$\cos x = -1 in$$ $$[0, 2\pi)$$?

Accepted Answer

$$x = \pi$$

Question 18

If $$	an x = 2$$ and $$x is in $$quadrant III, what is $$x$$?

Accepted Answer

$$x = \pi + \arctan(2)$$

Question 19

Which of the following is the correct solution for $$\sin x = 0 in$$ $$[0, 2\pi)$$?

Accepted Answer

$$x = 0, \pi$$

Question 20

Which of the following is the correct formula for $$\cos(\arcsin x)$$?

Accepted Answer

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

Trigonometric Identities, Inverse Functions, and Equations – Study Guide and Review

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