Question 1

Convert $$\frac{7\pi}{3}$$ radians to degrees.

Accepted Answer

$$420^\circ$$

Question 2

A belt runs a pulley of radius $$6 cm at$$ $$80$$ revolutions per minute. What is the angular speed of the pulley in radians per second?

Accepted Answer

$$8.38$$ radians/sec

Question 3

Find the area of a sector of a circle with radius $$r = 5$$ and central angle $$	heta = \frac{\pi}{3}$$ radians.

Accepted Answer

$$\frac{25\pi}{6}$$

Question 4

Convert $$120^\circ to $$radians. Leave your answer as a multiple of $$\pi.$$

Accepted Answer

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

Question 5

A bicycle tire has a radius of $$13.0 in. $$and turns at $$215$$ revolutions per minute. How fast is the bicycle traveling in miles per hour? ($$5280 ft$$ $$= 1 mi)$$

Accepted Answer

$$8.3$$ mph

Question 6

If $$\sin s = \frac{1}{2}$$ and $$s \in [0, 2\pi)$$, what are the possible values for $$s$$?

Accepted Answer

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

Question 7

A gear of radius $$4.8 in. is $$meshed with a gear of radius $$7.1 in. If $$the smaller gear rotates $$315^\circ$$, through how many degrees does the larger gear rotate?

Accepted Answer

$$213.1^\circ$$

Question 8

What is the period of the function $$y = 2 \cos\left(\frac{1}{2}x - \pi\right)$$?

Accepted Answer

$$4\pi$$

Question 9

Find the exact value of $$	an s if$$ $$s \in [\pi, 2\pi]$$ and $$	an s = \sqrt{3}.$$

Accepted Answer

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

Question 10

A clock’s minute hand is $$3 in. $$long. How far does the tip travel in $$30$$ minutes? (Leave answer as a multiple of $$\pi.)$$

Accepted Answer

$$3\pi in.$$

Question 11

Convert $$-315^\circ to $$radians. Leave your answer as a multiple of $$\pi.$$

Accepted Answer

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

Question 12

Given the point $$(-3, 4) on $$the terminal side of an angle $$	heta in $$standard position, find $$\sin 	heta.$$

Accepted Answer

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

Question 13

A sector of a circle has area $$10\pi$$ and radius $$10. $$What is the measure of the central angle in radians?

Accepted Answer

$$2$$

Question 14

What is the amplitude of the function $$y = -3 \sin(x) + 2$$?

Accepted Answer

$$3$$

Question 15

If $$\cos s = -\frac{1}{2}$$ and $$s \in [0, 2\pi)$$, what are the possible values for $$s$$?

Accepted Answer

$$\frac{2\pi}{3}, \frac{4\pi}{3}$$

Question 16

A Ferris wheel with a radius of $$50 ft $$revolves twice per minute. What is the linear speed of a seat on the edge in ft/min?

Accepted Answer

$$200\pi ft/$$min

Question 17

What is the period of the function $$y = 	an(2x)$$?

Accepted Answer

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

Question 18

Convert $$\frac{11\pi}{6}$$ radians to degrees.

Accepted Answer

$$330^\circ$$

Question 19

If $$\sin s = -\frac{\sqrt{3}}{2}$$ and $$s \in [0, 2\pi)$$, what are the possible values for $$s$$?

Accepted Answer

$$\frac{4\pi}{3}, \frac{5\pi}{3}$$

Question 20

A point on the edge of a gyroscope of radius $$83 cm is $$rotating $$680$$ times per minute. What is the linear speed in cm/min?

Accepted Answer

$$565,336 cm/$$min

Trigonometry Exam 2 Study Guide: Angle Conversion and Applications

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