Q: Which formula gives the area $$A of a $$sector of a circle with radius $$r$$ and central angle $$\theta (in $$radians)?

$$A = \frac{1}{2} r^2$ \theta$$

Question 1

Convert the following radian measure to degree measure: $$\frac{7\pi}{4}$$ radians.

Accepted Answer

$$315^\circ$$

Question 2

In which quadrant(s) does an angle $$\alpha$$ satisfy $$\sin \alpha \u003e 0$$ and $$\cos \alpha \u003c 0$$?

Accepted Answer

Quadrant II

Question 3

Find the exact value of $$\sin(-300^\circ).$$

Accepted Answer

$$\frac{1}{2}$$

Question 4

Find the exact value of $$\cos(-300^\circ).$$

Accepted Answer

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

Question 5

Evaluate $$2 	an 120^\circ + 5 \sin 150^\circ - \cos 180^\circ.$$

Accepted Answer

$$-2 \sqrt{3} + \frac{5}{2} - 1$$

Question 6

A plateau is $$20.2$$ meters high. If the angle of elevation to the top is $$12.5^\circ$$, how far are you from the base?

Accepted Answer

$$91.1$$ meters

Question 7

The tires of a bicycle have radius $$13.0 in. $$and are turning at $$225$$ revolutions per minute. How fast is the bicycle traveling in miles per hour? (Use $$5280 ft$$ $$= 1 mi)$$

Accepted Answer

$$17.4$$ mph

Question 8

Find the measure (in radians) of a central angle of a sector of area $$14$$ square inches in a circle of radius $$3.6$$ inches.

Accepted Answer

$$2.2$$ radians

Question 9

Suppose point $$P is on a $$circle with radius $$r = 8 in$$., angular speed $$\omega = \frac{\pi}{5}$$ rad/min, and $$t = 10$$ min. What is the angle generated by $$P in $$time $$t$$?

Accepted Answer

$$2\pi$$

Question 10

Suppose point $$P is on a $$circle with radius $$r = 8 in$$., angular speed $$\omega = \frac{\pi}{5}$$ rad/min, and $$t = 10$$ min. What is the distance traveled by $$P$$ along the circle in time $$t$$?

Accepted Answer

$$16\pi$$ inches

Question 11

Suppose point $$P is on a $$circle with radius $$r = 8 in$$., angular speed $$\omega = \frac{\pi}{5}$$ rad/min. What is the linear speed of $$P$$?

Accepted Answer

$$\frac{8\pi}{5}$$ inches/min

Question 12

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

Accepted Answer

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

Question 13

A car travels from City A to City B at a bearing of $$N\ 48^\circ\ E$$ for $$1.8$$ hours at $$55$$ mph, then from City B to City C at a bearing of $$S\ 42^\circ\ E$$ for $$1.6$$ hours at $$55$$ mph. What is the approximate distance from City A to City C?

Accepted Answer

$$132$$ miles

Question 14

Which formula gives the area $$A of a $$sector of a circle with radius $$r$$ and central angle $$	heta (in $$radians)?

Accepted Answer

$$A = \frac{1}{2} r^2$ 	heta$$

Question 15

If $$\sin 	heta = \frac{1}{2}$$ and $$	heta is in $$Quadrant II, what is $$\cos 	heta$$?

Accepted Answer

$$-\frac{\sqrt{3}}{2}$$

Question 16

A wheel with radius $$r$$ rotates at angular speed $$\omega. $$What is the formula for the linear speed $$v$$?

Accepted Answer

$$v = r \omega$$

Question 17

If $$\cos 	heta = -\frac{1}{2}$$ and $$	heta is in $$Quadrant III, what is $$\sin 	heta$$?

Accepted Answer

$$-\frac{\sqrt{3}}{2}$$

Question 18

Which identity expresses $$\sin(A+B) in $$terms of $$\sin A$$, $$\cos A$$, $$\sin B$$, and $$\cos B$$?

Accepted Answer

$$\sin(A+B) = \sin A \cos B + \cos A \sin B$$

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