Question 1

What is the exact radian value of $$\arccos(0.5)$$?

Accepted Answer

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

Question 2

Given $$\sec \beta = 3$$ and $$-\frac{\pi}{2} \u003c \beta \u003c 0$$, what is $$\sin \beta$$?

Accepted Answer

$$-\frac{2\sqrt{2}}{3}$$

Question 3

If the terminal side of angle $$\alpha in $$standard position passes through $$(3, -4)$$, what is $$	an \alpha$$?

Accepted Answer

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

Question 4

Simplify $$	an x + \cot x in $$terms of sines and cosines.

Accepted Answer

$$\frac{\sin^2$ x + \cos^2$ x}{\sin x \cos x}$$

Question 5

Determine whether $$f(x) = \sin x + 	an x is $$odd, even, or neither.

Accepted Answer

Odd

Question 6

What is the exact value of $$\sin$$^{-1}$$\left(\frac{\sqrt{3}}{2}\right)$$?

Accepted Answer

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

Question 7

Given $$\cot x \cos^2$ x - \cot x$$, factor the expression.

Accepted Answer

$$\cot x (\cos^2$ x - 1)$$

Question 8

Prove the identity: $$\cos x \sin^2$ x + \cos^3$ x \over \sin x = \cot x. $$Which step is correct?

Accepted Answer

Combine numerator: $$\cos x (\sin^2$ x + \cos^2$ x)$$

Question 9

A child looks up at a 150 ft building with an angle of elevation of $$76^\circ$$, then walks away and looks up at $$34^\circ. $$How far did the child walk?

Accepted Answer

Approximately 170.2 ft

Question 10

From the top of an 80 m cliff, the angle of depression to a marker on the ocean is $$20^\circ. $$How far is the marker from the foot of the cliff?

Accepted Answer

Approximately 219.7 m

Question 11

What is the exact value of $$\sin(\sec$$^{-1}$$(-\sqrt{2}))$$?

Accepted Answer

$$-\frac{\sqrt{2}}{2}$$

Question 12

If $$a = 2$$ and $$b = 3 in a $$right triangle, what is the length of the hypotenuse $$c$$?

Accepted Answer

$$\sqrt{13}$$

Question 13

Given $$c = 14$$ and $$\alpha = 17^\circ in a $$right triangle, what is the length of side $$a$$ opposite $$\alpha$$?

Accepted Answer

Approximately $$4.1$$

Question 14

What is the radian measure of $$\cot$$^{-1}$$(0) in $$degrees?

Accepted Answer

$$90^\circ$$

Question 15

Simplify $$\sec x \cot x in $$terms of sines and cosines.

Accepted Answer

$$\frac{1}{\sin x}$$

Question 16

If $$\alpha is an $$angle in standard position whose terminal side contains $$(3, 7)$$, what is $$\sin \alpha$$?

Accepted Answer

$$\frac{7}{\sqrt{58}}$$

Question 17

What is the exact value of $$	an$$^{-1}$$(1) in $$radians?

Accepted Answer

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

Question 18

Which of the following is the correct simplification for $$\frac{\sin x}{\cos(-x)} + \frac{\sin(-x)}{\cos x}$$?

Accepted Answer

$$0$$

Question 19

Given $$\sin^4$ x - \sin^2$ x$$ divided by $$\sec x$$, what is the simplified form?

Accepted Answer

$$\sin^2$ x (\sin^2$ x - 1) \cos x$$

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