Q: A sector of a circle has a radius of 12 m and a central angle of $$\frac{\pi}{6}$$ radians. What is the area of the sector?

$$12 m$^2 ($$since $$A = \frac{1}{2} r^2$ \theta = \frac{1}{2} \times 12^2$ \times \frac{\pi}{6} = 12\pi m$^2)$$

Question 1

Which of the following best describes a quadrantal angle?

Accepted Answer

An angle whose terminal side lies along the x- or y-axis in standard position.

Question 2

A central angle in a circle of radius 10 cm intercepts an arc of length 15 cm. What is the measure of the angle in radians?

Accepted Answer

$$1.5$$

Question 3

Convert $$225^ to $$radians.

Accepted Answer

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

Question 4

Two angles are supplementary. If one angle measures $$x$$ degrees, what is the measure of its supplement?

Accepted Answer

$$180^ - x$$

Question 5

A sector of a circle has a radius of 12 m and a central angle of $$\frac{\pi}{6}$$ radians. What is the area of the sector?

Accepted Answer

$$12 m$^2 ($$since $$A = \frac{1}{2} r^2$ 	heta = \frac{1}{2} 	imes 12^2$ 	imes \frac{\pi}{6} = 12\pi m$^2)$$

Question 6

A belt runs a pulley of radius 8 cm at 60 revolutions per minute. What is the angular speed of the pulley in radians per second?

Accepted Answer

$$2\pi$$ radians/second

Question 7

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

Accepted Answer

$$s = r	heta$$

Question 8

If the latitude of City A is $$52^ N $$and City B is $$40^ N$$, and the radius of Earth is 6371 km, what is the north-south distance between the two cities? (Use $$s = r	heta$$ and convert degrees to radians.)

Accepted Answer

$$1333 km$$

Question 9

Convert $$2.5$$ radians to degrees.

Accepted Answer

$$143.24^$$

Question 10

A point moves along a circle of radius 5 m with an angular speed of $$3$$ radians per second. What is its linear speed?

Accepted Answer

$$15 m/s$$

Question 11

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

Accepted Answer

$$315^$$

Question 12

Convert $$120^ to $$radians.

Accepted Answer

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

Question 13

A sector of a circle has an area of $$25\pi m$^2$$ and a central angle of $$\frac{\pi}{2}$$ radians. What is the radius of the circle?

Accepted Answer

$$10 m$$

Question 14

If an angle is $$3\pi$$ radians, what is its measure in degrees?

Accepted Answer

$$540^$$

Question 15

Which of the following is NOT a property of coterminal angles?

Accepted Answer

They always have the same degree measure.

Question 16

A clock's minute hand is 12 cm long. How far does the tip of the minute hand travel in 20 minutes?

Accepted Answer

$$16\pi cm$$

Question 17

What is the degree measure of an angle whose radian measure is $$\frac{5\pi}{6}$$?

Accepted Answer

$$150^$$

Question 18

A wheel of radius 0.5 m rotates at 120 revolutions per minute. What is the linear speed of a point on the rim in meters per second?

Accepted Answer

$$2\pi m/s$$

Question 19

Convert $$75^ 30' 0'' to $$decimal degrees.

Accepted Answer

$$75.5^$$

Angles, Arc, and Their Measures: Trigonometry Functions and Applications (Chapter 9.1 Study Notes)

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