Q: Factor the following expression: $$5 \cos^2$ x \sin^2$ x - 12 \cos x \sin \theta + 4 \sin \theta.$$

$$(\sin \theta)(5 \cos^2$ x \sin x - 12 \cos x + 4)$$

Question 1

Which of the following is the exact value of $$\arccos(0.5) in $$radians?

Accepted Answer

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

Question 2

Evaluate $$\sin(\sec$$^{-1}$$(-\sqrt{2})).$$

Accepted Answer

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

Question 3

Find the exact value in degrees of $$\arccos(0).$$

Accepted Answer

$$90^\circ$$

Question 4

If $$\sec 	heta = 3$$ and $$\frac{\pi}{2} \u003c 	heta \u003c \pi$$, what is $$\sin 	heta$$?

Accepted Answer

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

Question 5

A point $$(3, -4)$$ lies on the terminal side of an angle $$	heta in $$standard position. What is $$	an 	heta$$?

Accepted Answer

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

Question 6

Simplify $$\frac{\sin^2$ x - \sin^4$ x}{\sin^2$ x}.$$

Accepted Answer

$$1 - \sin^2$ x$$

Question 7

Which of the following expressions is equivalent to $$	an x + \cot x$$?

Accepted Answer

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

Question 8

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

Accepted Answer

Odd

Question 9

Factor the following expression: $$5 \cos^2$ x \sin^2$ x - 12 \cos x \sin 	heta + 4 \sin 	heta.$$

Accepted Answer

$$(\sin 	heta)(5 \cos^2$ x \sin x - 12 \cos x + 4)$$

Question 10

Solve the right triangle where $$b = 7$$, $$c = 14. $$What is the value of $$a$$?

Accepted Answer

$$a = 7 \sqrt{2}$$

Question 11

A vertical cliff is 80 meters above the surface of the ocean. The angle of depression to a marker on the surface is $$20^\circ. $$How far is the marker from the foot of the cliff?

Accepted Answer

$$219.7$$ meters

Question 12

Find the radian measure of an angle whose terminal side contains the point $$(3, 7)$$ and $$0 \u003c \alpha \u003c 2\pi. $$Round to the nearest hundredth.

Accepted Answer

$$1.17$$ 	ext{ radians}$

Question 13

Which of the following is the correct simplification of $$	an^2$(x) - \sec^2$(x) + 1$$?

Accepted Answer

$$0$$

Question 14

If $$\sin(	heta) = -0.5$$ and $$\pi \u003c 	heta \u003c \frac{3\pi}{2}$$, what is $$	heta$$?

Accepted Answer

$$\frac{7\pi}{6}$$

Question 15

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

Accepted Answer

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

Question 16

Given $$f(x) = \frac{\sin x}{x}$$, determine if $$f(x) is $$even, odd, or neither.

Accepted Answer

Even

Question 17

Which of the following is the correct value for $$\arccot(1) in $$radians?

Accepted Answer

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

Question 18

A child on a sidewalk looks up at a building that is 150 ft tall with an angle of elevation of $$76^\circ. $$The child walks away from the building and the angle of elevation decreases to $$45^\circ. $$How far did the child walk?

Accepted Answer

$$150(\cot 45^\circ - \cot 76^\circ)$$

Precalculus Trigonometry: Functions, Identities, and Applications Study Notes

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