Question 1

A circle has a radius of $$2$$ yards and an arc length of $$3$$ yards. What is the radian measure of the central angle that intercepts this arc?

Accepted Answer

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

Question 2

Convert $$144^\circ to $$radians. Express your answer in terms of $$\pi.$$

Accepted Answer

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

Question 3

Convert $$\frac{4\pi}{3}$$ radians to degrees.

Accepted Answer

$$240^\circ$$

Question 4

Which of the following graphs shows the angle $$-\frac{\pi}{4} in $$standard position?

Accepted Answer

Image 4

Question 5

Find a positive angle less than $$360^\circ$$ that is coterminal with $$515^\circ.$$

Accepted Answer

$$155^\circ$$

Question 6

Find a positive angle less than $$2\pi$$ that is coterminal with $$\frac{33\pi}{4}.$$

Accepted Answer

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

Question 7

The minute hand of a clock moves from 12 to 4 o'clock. Through how many degrees does it move?

Accepted Answer

$$120^\circ$$

Question 8

Given $$\sin t = \frac{2}{5}$$ and $$t is $$acute, find $$\cos t.$$

Accepted Answer

$$\frac{\sqrt{21}}{5}$$

Question 9

Suppose a right triangle has legs $$a = 9$$ and hypotenuse $$c = 41. $$What is the length of the other leg $$b$$?

Accepted Answer

$$40$$

Question 10

Evaluate $$\csc 45^\circ$$ and rationalize the denominator.

Accepted Answer

$$\sqrt{2}$$

Question 11

Rewrite $$\sin 15^\circ in $$terms of its cofunction.

Accepted Answer

$$\cos 75^\circ$$

Question 12

A tower is $$106$$ feet tall and casts a shadow $$134$$ feet long. What is the angle of elevation of the sun to the nearest degree?

Accepted Answer

$$38^\circ$$

Question 13

A road is inclined at $$7^\circ. $$After driving $$5100$$ feet along this road, what is the driver's increase in altitude (to the nearest foot)?

Accepted Answer

$$622$$ feet

Question 14

Given the point $$(-24, 7) on $$the terminal side of angle $$	heta$$, find $$\sin 	heta.$$

Accepted Answer

$$-\frac{7}{25}$$

Question 15

If $$\cos 	heta \u003e 0$$ and $$\sin 	heta \u003e 0$$, in which quadrant does $$	heta$$ lie?

Accepted Answer

Quadrant I

Question 16

Find the reference angle for $$204^\circ.$$

Accepted Answer

$$24^\circ$$

Question 17

Determine the amplitude and period of $$y = -4 \sin \frac{x}{4}.$$

Accepted Answer

Amplitude: $$4$$, Period: $$8\pi$$

Question 18

Find the exact value of $$\cos$$^{-1}$$\left(\frac{3}{2}\right).$$

Accepted Answer

Undefined

Question 19

A boat leaves a harbor and travels $$175$$ miles on a bearing of $$N\ 51^\circ\ E. $$How many miles north has the boat traveled? (Round to the nearest tenth.)

Accepted Answer

$$110.1$$ miles

Question 20

Use the identity $$\sin^2$ 	heta + \cos^2$ 	heta = 1 to $$find $$\cos 	heta if$$ $$\sin 	heta = \frac{2}{9}$$ and $$	heta is $$acute.

Accepted Answer

$$\frac{\sqrt{77}}{9}$$

Drawing Angles in Standard Position and Identifying Quadrants

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