Question 1

Convert $$75^\circ to $$radians.

Accepted Answer

$$\frac{5\pi}{12}$$

Question 2

Convert $$-\frac{7\pi}{6}$$ radians to degrees.

Accepted Answer

$$-210^\circ$$

Question 3

Find the exact value of $$\cos\left(\frac{4\pi}{3}\right).$$

Accepted Answer

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

Question 4

A sector of a circle has a radius of $$8 cm $$and a central angle of $$315^\circ. $$What is the arc length of the sector? (Use $$\pi in $$your answer.)

Accepted Answer

$$14\pi/4 cm$$

Question 5

A sector of a circle has a radius of $$13 ft $$and a central angle of $$\frac{3\pi}{4}$$ radians. What is the area of the sector?

Accepted Answer

$$\frac{169\pi}{8} ft$^2$$

Question 6

A windshield wiper wipes through an angle of $$120^\circ$$ and clears an area of $$368$$ square inches. How long is the windshield wiper (radius)?

Accepted Answer

$$18 in$$

Question 7

A circular pool has a diameter of $$20$$ meters and a walkway of width $$2$$ meters around it. If a bag of wood chips covers $$5 m$^2$$, how many bags are needed to cover the walkway?

Accepted Answer

$$28$$

Question 8

Find all $$s in$$ $$[0, 2\pi)$$ such that $$	an s = -\sqrt{3}.$$

Accepted Answer

$$\frac{2\pi}{3}, \frac{5\pi}{3}$$

Question 9

A wind machine has blades $$10 ft $$long and rotates at $$4$$ revolutions per second. What is the linear speed of the blade tips in ft/min?

Accepted Answer

$$800\pi ft/$$min

Question 10

A bicycle wheel with radius $$13.0 in. $$turns with angular velocity $$3$$ radians/sec. What distance does a point on the tire travel in $$1$$ minute?

Accepted Answer

$$2340 in$$

Question 11

For the function $$y = 2\sin(x + \pi)$$, what is the amplitude, period, and phase shift?

Accepted Answer

Amplitude: $$2$$, Period: $$2\pi$$, Phase shift: $$-\pi$$

Question 12

For the function $$y = 2 + \cos 3x$$, what is the vertical translation and period?

Accepted Answer

Vertical translation: $$2$$, Period: $$\frac{2\pi}{3}$$

Question 13

Which of the following is the correct equation for the arc length $$s of a $$circle with radius $$r$$ and central angle $$	heta (in $$radians)?

Accepted Answer

$$s = r	heta$$

Question 14

Given $$y = -2\sin(2x + \pi)$$, what is the amplitude and period?

Accepted Answer

Amplitude: $$2$$, Period: $$\pi$$

Question 15

If $$\cos 2s = \frac{3}{4}$$ and $$s \in [-\pi, \pi)$$, which of the following is a possible value for $$s$$?

Accepted Answer

$$\frac{1}{2}\arccos\left(\frac{3}{4}\right)$$

Arc Length and Area of a Sector – Step-by-Step Guidance

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