Q: A gear rotates 300 times per minute. What is its angular speed in radians per second?

$$\frac{300 \times 2\pi}{60} = 10\pi$$ radians/sec

Q: What is the domain of the function $$y = \tan(x)$$?

$$x \neq \frac{\pi}{2} + n\pi,\ n \in \mathbb{Z}$$

Question 1

What is the exact value of $$\sin\left(\frac{\pi}{3}\right)$$?

Accepted Answer

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

Question 2

A bicycle tire has a radius of 13 inches and rotates at 275 revolutions per minute. What is the linear speed of the bicycle in miles per hour? (1 mile = 5280 feet)

Accepted Answer

$$\approx 17.0$$ mph

Question 3

Convert $$37.2^\circ to $$radians.

Accepted Answer

$$0.649$$ radians$

Question 4

If a point $$P$$ moves on a circle of radius $$r = 10 cm $$with angular speed $$\omega = \frac{\pi}{12}$$ radians/sec for $$t = 6$$ seconds, what is the distance traveled by $$P$$ along the circle?

Accepted Answer

$$5\pi cm$$

Question 5

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

Accepted Answer

$$\pi$$

Question 6

A gear rotates 300 times per minute. What is its angular speed in radians per second?

Accepted Answer

$$\frac{300 	imes 2\pi}{60} = 10\pi$$ radians/sec

Question 7

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

Accepted Answer

$$x 
eq \frac{\pi}{2} + n\pi,\ n \in \mathbb{Z}$$

Question 8

A rope is wound around a drum of radius $$0.764$$ feet through an angle of $$37.2^\circ. $$How much rope is wound? (Give your answer in feet, rounded to three decimals.)

Accepted Answer

$$0.497 ft$$

Question 9

What is the amplitude of the function $$y = -2\sin\left(x - \frac{\pi}{4}\right)$$?

Accepted Answer

$$2$$

Question 10

If the minute hand of a clock completes one revolution in 60 minutes, what is its angular speed in radians per minute?

Accepted Answer

$$\frac{\pi}{30}$$ radians/min

Question 11

What is the exact value of $$	an\left(-\frac{\pi}{6}ight)$$?

Accepted Answer

$$-\frac{1}{\sqrt{3}}$$

Question 12

A sector of a circle has a radius of 251 meters and a central angle of $$15^\circ. $$What is the area of the sector? (Use $$A = \frac{1}{2} r^2$ 	heta$$ with $$	heta in $$radians.)

Accepted Answer

$$4125 m$^2$$

Question 13

What is the phase shift of the function $$y = 3\sin\left(x + \frac{\pi}{3}\right)$$?

Accepted Answer

$$\frac{\pi}{3}$$ units to the left

Question 14

If the larger pulley has a radius of 15 cm and rotates at 24 revolutions per second, what is its angular speed?

Accepted Answer

$$48\pi$$ radians/sec

Question 15

What is the value of $$\sec\left(\frac{\pi}{2}\right)$$?

Accepted Answer

Undefined

Question 16

A bicycle pedal gear of radius 4.80 inches is connected to a rear gear of radius 1.50 inches. If the pedals rotate through $$270^\circ$$, how far does the bicycle move (in inches)?

Accepted Answer

$$22.62$$ inches

Question 17

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

Accepted Answer

$$4\pi$$

Question 18

What is the value of $$\cos\left(\frac{5\pi}{6}\right)$$?

Accepted Answer

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

Question 19

If a gear rotates 120 times in half an hour, what is its angular speed in radians per minute?

Accepted Answer

$$4\pi$$ radians/min

Question 20

Which of the following is the correct formula for the arc length $$s of a $$circle of radius $$r$$ subtended by a central angle $$	heta (in $$radians)?

Accepted Answer

$$s = r	heta$$

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