Question 1

What is the supplement of an angle measuring $$27^	ext{\circ}$$?

Accepted Answer

$$153^	ext{\circ}$$

Question 2

An angle of $$1182^	ext{\circ} is in $$which quadrant when drawn in standard position?

Accepted Answer

Quadrant III

Question 3

Which angle is coterminal with $$-1363^	ext{\circ}$$?

Accepted Answer

$$167^	ext{\circ}$$

Question 4

The terminal side of angle $$\beta$$ passes through the point $$(-3, -5). $$What is $$\sin \beta$$?

Accepted Answer

$$\sin \beta = \frac{-5}{\sqrt{34}}$$

Question 5

If $$	an \beta = -7$$ and the terminal side of $$\beta$$ lies in quadrant II, what are the exact values of $$\sin \beta$$ and $$\cos \beta$$?

Accepted Answer

$$\sin \beta = \frac{7}{\sqrt{50}},\ \cos \beta = -\frac{1}{\sqrt{50}}$$

Question 6

A restaurant at the top of the Stratosphere Tower completes a full revolution in one hour. How many radians does it rotate in 56 minutes?

Accepted Answer

$$\frac{14\pi}{15}$$

Question 7

Given $$	an 	heta = -\sqrt{3}$$ and $$	heta is in $$Quadrant II, what is the reference angle for $$	heta$$?

Accepted Answer

$$60^	ext{\circ}$$

Question 8

Find the reference angle for $$\frac{10\pi}{7} in $$radians and degrees.

Accepted Answer

$$\frac{3\pi}{7}$$\ and\ $$77.14^	ext{\circ}$$

Question 9

If the terminal side of angle $$	heta$$ intersects the unit circle at $$\left(-\frac{24}{25}, -\frac{7}{25}ight)$$, what is $$	an 	heta$$?

Accepted Answer

Question 10

Find the area of a circular sector with diameter $$4.8 cm $$and central angle $$\sigma = 330^	ext{\circ}. $$Round your answer to three significant digits.

Accepted Answer

$$19.9\ 	ext{cm}^2$$

Question 11

A point travels along a circle with radius $$6 km $$for $$t = 10$$ seconds, given angular velocity $$\omega = \frac{\pi}{15}$$ rad/sec. What is the distance $$s$$ traveled?

Accepted Answer

$$4\pi$$\ km

Question 12

If $$\cos 	heta = -\frac{1}{2}$$ and $$	an 	heta is $$positive, what is the exact value of $$	heta$$?

Accepted Answer

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

Question 13

Simplify $$2\pi - \frac{\pi}{3}$$ and convert to degrees.

Accepted Answer

$$\frac{5\pi}{3}$$\ and\ $$300^	ext{\circ}$$

Question 14

For the function $$y = 1 - 3\cos(2x - \frac{\pi}{2})$$, what is the amplitude?

Accepted Answer

$$3$$

Question 15

For the function $$y = 1 - 3\cos(2x - \frac{\pi}{2})$$, what is the period?

Accepted Answer

$$\pi$$

Question 16

For the function $$y = 2	an(-x + \frac{\pi}{2})$$, what is the period?

Accepted Answer

$$\pi$$

Question 17

For the function $$y = 2\sec(2x)$$, what are the vertical asymptotes in the interval $$-\pi \u003c x \u003c \pi$$?

Accepted Answer

$$x = -\frac{\pi}{2},\ 0,\ \frac{\pi}{2}$$

Question 18

Given the graph with points $$(0, 4)$$, $$(\pi, -2)$$, and $$(-\pi, -2)$$, which equation best fits the graph?

Accepted Answer

$$f(x) = -3\cos(x) + 2$$

Precalculus Lab 2 Study Guide: Trigonometry, Angles, and Graphs

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