Q: Find the exact value of $$\\sin(75^\\circ)$$ using sum and difference formulas.

$$\\frac{\\sqrt{6} + \\sqrt{2}}{4}$$

Q: Solve for $$x in$$ $$2\\sin(x) - 1 = 0$$ for $$0 \\leq x \u003c 2\\pi.$$

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

Q: A sound wave can be modeled by $$y = 3\\sin(2t). $$What is the amplitude and period of this wave?

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

Q: Given $$A = 30^\\circ$$, $$b = 10$$, and $$a = 5$$, use the Law of Sines to find $$B.$$

$$B = \\arcsin(1) (no $$solution)

Q: Express $$\\sin(x)\\cos(y) as a $$sum using product-to-sum formulas.

$$\\frac{1}{2}[\\sin(x+y) + \\sin(x-y)]$$

Q: Solve for $$x$$: $$\\cos^2$(x) = \\frac{1}{4}$$ for $$0 \\leq x \u003c 2\\pi.$$

$$x = \\frac{\\pi}{3}, \\frac{2\\pi}{3}, \\frac{4\\pi}{3}, \\frac{5\\pi}{3}$$

Q: Which of the following is the correct identity for $$\\tan(x+y)$$?

$$\\frac{\\tan(x) + \\tan(y)}{1 - \\tan(x)\\tan(y)}$$

Question 1

Convert $$135^\circ to $$radians.

Accepted Answer

$$\frac{5\pi}{4}$$

Question 2

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

Accepted Answer

$$10\pi$$ meters

Question 3

Given $$\sin(\theta) = \frac{3}{5}$$ and $$\theta is in $$Quadrant II, find $$\cos(\theta).$$

Accepted Answer

$$-\frac{4}{5}$$

Question 4

Find the exact value of $$\sin(75^\circ)$$ using sum and difference formulas.

Accepted Answer

$$\frac{\sqrt{6} + \sqrt{2}}{4}$$

Question 5

Which of the following is the period of the function $$y = 2\cos(3x)$$?

Accepted Answer

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

Question 6

Solve for $$x in$$ $$2\sin(x) - 1 = 0$$ for $$0 \leq x \u003c 2\pi.$$

Accepted Answer

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

Question 7

A sound wave can be modeled by $$y = 3\sin(2t). $$What is the amplitude and period of this wave?

Accepted Answer

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

Question 8

Find the reference angle for $$210^\circ.$$

Accepted Answer

$$30^\circ$$

Question 9

If $$\tan(\theta) = -1$$ and $$\theta is in $$Quadrant IV, what is $$\theta in $$radians?

Accepted Answer

$$\frac{7\pi}{4}$$

Question 10

Given $$A = 30^\circ$$, $$b = 10$$, and $$a = 5$$, use the Law of Sines to find $$B.$$

Accepted Answer

$$B = \arcsin(1) (no $$solution)

Question 11

Express $$\sin(x)\cos(y) as a $$sum using product-to-sum formulas.

Accepted Answer

$$\frac{1}{2}[\sin(x+y) + \sin(x-y)]$$

Question 12

Convert the rectangular coordinates $$(-1, \sqrt{3}) to $$polar coordinates.

Accepted Answer

$$(2, \frac{2\pi}{3})$$

Question 13

Which of the following is an even trigonometric function?

Accepted Answer

$$\cos(x)$$

Question 14

Find the magnitude of the vector $$\vec{v} = 3\mathbf{i} - 4\mathbf{j}.$$

Accepted Answer

$$5$$

Question 15

If $$y = 2\sin(\pi t)$$ models the height (in meters) of a mass on a spring, what is the period of oscillation?

Accepted Answer

$$2$$

Question 16

Solve for $$x$$: $$\cos^2$(x) = \frac{1}{4}$$ for $$0 \leq x \u003c 2\pi.$$

Accepted Answer

$$x = \frac{\pi}{3}, \frac{2\pi}{3}, \frac{4\pi}{3}, \frac{5\pi}{3}$$

Question 17

Which of the following is the correct double-angle formula for $$\sin(2x)$$?

Accepted Answer

$$2\sin(x)\cos(x)$$

Question 18

A vector has magnitude $$10$$ and direction $$60^\circ. $$What are its rectangular components?

Accepted Answer

$$(5, 5\sqrt{3})$$

Question 19

Which of the following is the correct identity for $$\tan(x+y)$$?

Accepted Answer

$$\frac{\tan(x) + \tan(y)}{1 - \tan(x)\tan(y)}$$

College Trigonometry (MAC 1114C) Syllabus & Study Guide

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