Q: Which of the following is the correct domain for the function $$\tan \theta$$?

$$\theta \neq k\dfrac{\pi}{2}$$, where $$k is $$any odd integer

Q: Solve for $$\theta in$$ $$[0, 2\pi)$$: $$2\cos^2$\theta + \cos\theta = 0.$$

$$\theta = \pi, \dfrac{2\pi}{3}, \dfrac{4\pi}{3}$$

Q: Which of the following is the general solution to $$\tan \theta = -1$$?

$$\theta = -\dfrac{\pi}{4} + k\pi,\ k \in \mathbb{Z}$$

Question 1

Convert $$150^\circ to $$radians.

Accepted Answer

$$\dfrac{5\pi}{6}$$

Question 2

A circular track has a radius of $$20$$ meters. What is the length of the arc subtended by a central angle of $$60^\circ$$?

Accepted Answer

$$\dfrac{20\pi}{3}$$ meters

Question 3

Given $$\sin 	heta = \dfrac{3}{5}$$ and $$\cos 	heta = -\dfrac{4}{5}$$, which quadrant is $$	heta in$$?

Accepted Answer

Quadrant II

Question 4

Find the exact value of $$\cos\left(\dfrac{5\pi}{6}\right).$$

Accepted Answer

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

Question 5

Which of the following is the correct domain for the function $$	an 	heta$$?

Accepted Answer

$$	heta 
eq k\dfrac{\pi}{2}$$, where $$k is $$any odd integer

Question 6

What is the amplitude and period of $$f(x) = 3 \sin(2x)$$?

Accepted Answer

Amplitude: $$3$$, Period: $$\pi$$

Question 7

Solve for $$	heta in$$ $$[0, 2\pi)$$: $$2\cos^2$	heta + \cos	heta = 0.$$

Accepted Answer

$$	heta = \pi, \dfrac{2\pi}{3}, \dfrac{4\pi}{3}$$

Question 8

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

Accepted Answer

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

Question 9

Which of the following identities is correct?

Accepted Answer

$$	an^2$ x + 1 = \sec^2$ x$$

Question 10

A Ferris wheel has a radius of $$10$$ meters. If a passenger travels along an arc of $$\dfrac{\pi}{2}$$ radians, what is the area of the sector swept out?

Accepted Answer

$$25\pi$$ square meters

Question 11

Find the exact value of $$\sin\left(\arccos\left(\dfrac{3}{5}\right)\right).$$

Accepted Answer

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

Question 12

Which of the following best describes the range of $$\sec 	heta$$?

Accepted Answer

$$(-\infty, -1] \cup [1, \infty)$$

Question 13

If $$f(x) = 2\sin(\pi x - \pi)$$, what is the phase shift?

Accepted Answer

$$1$$

Question 14

Solve for $$x$$: $$3\arccos x = \pi.$$

Accepted Answer

$$x = \dfrac{1}{2}$$

Question 15

Which of the following is an even function?

Accepted Answer

$$\cos x$$

Question 16

Evaluate $$\arctan(\sqrt{3}).$$

Accepted Answer

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

Question 17

Which of the following is the general solution to $$	an 	heta = -1$$?

Accepted Answer

$$	heta = -\dfrac{\pi}{4} + k\pi,\ k \in \mathbb{Z}$$

Question 18

Which of the following identities is true for all $$x in $$the domain?

Accepted Answer

$$\cos(-x) = \cos x$$

Question 19

If $$\sin 	heta = 0.4$$ and $$0 \leq 	heta \u003c 2\pi$$, how many solutions are there for $$	heta$$?

Accepted Answer

2

Trigonometric Functions, Properties, Graphs, Inverses, and Identities: Precalculus Study Guide

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