Q: Which of the following is the correct formula for 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

Which of the following best describes a radian?

Accepted Answer

A radian is the measure of an angle that subtends an arc equal to the radius of the circle.

Question 2

If an angle measures $$135\ ^\circ$$, in which quadrant does its terminal side lie?

Accepted Answer

Quadrant II

Question 3

Convert $$240\ ^\circ to $$radians. Express your answer in exact form.

Accepted Answer

$$\frac{4\pi}{3}$$

Question 4

Which formula is used to find the arc length $$s of a $$circle with radius $$r$$ and central angle $$	heta in $$radians?

Accepted Answer

$$s = r	heta$$

Question 5

A child is spinning a rock at the end of a $$2-$$foot rope at the rate of $$150$$ revolutions per minute. What is the angular speed in radians per second?

Accepted Answer

$$15.71$$ radians/sec$

Question 6

Convert $$\frac{5\pi}{6}$$ radians to degrees. Round to two decimal places.

Accepted Answer

$$150.00\ ^\circ$$

Question 7

Which of the following is the correct formula for 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 8

An angle in standard position has its terminal side in Quadrant III. Which of the following could be its measure?

Accepted Answer

$$210\ ^\circ$$

Question 9

What is the degree measure of $$\frac{7\pi}{4}$$ radians?

Accepted Answer

$$315\ ^\circ$$

Question 10

A sector of a circle has a radius of $$5 cm $$and a central angle of $$40\ ^\circ. $$What is the area of the sector? (Round to two decimal places)

Accepted Answer

$$8.73 cm$^2$$

Question 11

Which of the following is NOT a correct way to convert degrees to radians?

Accepted Answer

Multiply degrees by $$\frac{180}{\pi}$$

Question 12

If the linear speed $$v of an $$object moving in a circle of radius $$r is $$given by $$v = r\omega$$, what does $$\omega$$ represent?

Accepted Answer

Angular speed in radians per unit time

Question 13

Which of the following angles is coterminal with $$45\ ^\circ$$?

Accepted Answer

$$405\ ^\circ$$

Question 14

Express $$62.4\ ^\circ in $$degrees, minutes, and seconds (DMS). Round to the nearest second.

Accepted Answer

$$62\ ^\circ 24' 0''$$

Question 15

Which of the following statements about angles in standard position is TRUE?

Accepted Answer

The initial side is always on the positive $$x-$$axis.

Question 16

A right angle is equivalent to how many radians?

Accepted Answer

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

Question 17

If an angle is negative, which direction does its terminal side rotate from the initial side?

Accepted Answer

Clockwise

Question 18

What is the radian measure of $$90\ ^\circ$$?

Accepted Answer

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

Question 19

Which of the following is the correct conversion from $$2$$ radians to degrees?

Accepted Answer

$$114.59\ ^\circ$$

Question 20

A ray is defined as:

Accepted Answer

A part of a line that has one endpoint and extends indefinitely in one direction.

Angles and Their Measure: Trigonometric Functions and Applications

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