Question 1

Which of the following is the correct radian measure for the angle located at 120° on the unit circle?

Accepted Answer

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

Question 2

A weather radar scans a sector with a central angle of $$75^\circ$$ and a radius of 30 miles. What is the area scanned, in square miles? (Use $$A = \frac{	heta}{360^\circ} \pi r^2$ and round to the nearest hundredth.)

Accepted Answer

$$589.05$$

Question 3

Convert $$225^\circ to $$radians. What is the exact value?

Accepted Answer

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

Question 4

Which of the following angles is coterminal with $$-45^\circ$$?

Accepted Answer

$$315^\circ$$

Question 5

A bicycle with 27-inch diameter wheels is pedaled at 100 revolutions per minute. What is the speed in miles per hour? (Use $$C = \pi d$$ and $$1$$ mile $$= 63,360$$ inches. Round to the nearest hundredth.)

Accepted Answer

$$8.03$$

Question 6

If $$\sin 	heta = -\frac{3}{5}$$ and $$	heta is in $$Quadrant III, what is $$\cos 	heta$$?

Accepted Answer

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

Question 7

Convert $$42^\circ 7' 30'' to $$decimal degrees.

Accepted Answer

$$42.125^\circ$$

Question 8

A hiker stands 80 ft from a tree and sights the top at an angle of elevation of $$75^\circ. $$How tall is the tree to the nearest foot?

Accepted Answer

$$299$$

Question 9

Which quadrant contains the terminal side of an angle of $$210^\circ$$?

Accepted Answer

Quadrant III

Question 10

What is the reference angle for $$-135^\circ$$?

Accepted Answer

$$45^\circ$$

Question 11

If $$	an 	heta = 3$$ and $$	heta is in $$Quadrant II, what is $$\sin 	heta$$?

Accepted Answer

$$\frac{-3}{\sqrt{10}}$$

Question 12

Convert $$\frac{3\pi}{4}$$ radians to degrees. Round to the nearest hundredth.

Accepted Answer

$$135.00^\circ$$

Question 13

A point $$(2, -1)$$ lies on the terminal side of angle $$\alpha. $$What is $$\sin \alpha$$?

Accepted Answer

$$-\frac{1}{\sqrt{5}}$$

Question 14

What is the linear velocity (in miles per hour) of a point on the equator if the radius of the Earth is 3950 miles? (Assume one rotation per 24 hours, $$v = r\omega$$, $$\omega = \frac{2\pi}{24}$$ radians/hour.)

Accepted Answer

$$1034$$

Question 15

Which of the following is the decimal degree equivalent of $$18.125^\circ$$?

Accepted Answer

$$18^\circ 7' 30''$$

Question 16

If a record rotates at $$\frac{3\pi}{4}$$ radians per second, how many revolutions does a point on the edge make in 1 minute?

Accepted Answer

$$45$$

Question 17

Convert $$25 km/hr to m/s. (1 km = 1000 m$$, 1 hr = 3600 s)

Accepted Answer

$$6.9$$

Question 18

Which of the following pairs of angles are coterminal?

Accepted Answer

$$30^\circ$$ and $$390^\circ$$

Question 19

Find the central angle in degrees that intercepts an arc of 2000 miles on the surface of the Earth, given the radius is 3950 miles. (Use $$	heta = \frac{s}{r}$$, convert to degrees.)

Accepted Answer

$$29.01^\circ$$

Question 20

From a point on the street, the angle of elevation to the top of a building is $$65.7^\circ. $$From a point 100 feet closer, the angle is $$70.1^\circ. $$What is the height of the building to the nearest hundredth?

Accepted Answer

$$1117.04$$

Labeling Common Angles in Degrees and Radians on the Unit Circle

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