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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