Question 1

Which of the following best describes a quadrantal angle?

Accepted Answer

An angle whose terminal side lies on the x-axis or y-axis.

Question 2

What is the radian measure of a central angle that intercepts an arc equal in length to the radius of the circle?

Accepted Answer

$1$ radian

Question 3

Convert $270^{\circ}$ to radians.

Accepted Answer

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

Question 4

A circle has a radius of $8$ inches. Find the length of the arc intercepted by a central angle of $45^{\circ}$. Express your answer in inches rounded to two decimal places.

Accepted Answer

$8.38$ inches

Question 5

Which formula is used to find the area 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 6

If a point moves on a circle of radius $r$ through an angle of $	heta$ radians in time $t$, what is the formula for linear speed $v$?

Accepted Answer

$v = \frac{r 	heta}{t}$

Question 7

What is the degree measure of $\frac{5\pi}{6}$ radians?

Accepted Answer

$150^{\circ}$

Question 8

Which of the following angles is coterminal with $400^{\circ}$?

Accepted Answer

$40^{\circ}$

Question 9

A 45-rpm record has an angular speed of $45$ revolutions per minute. What is its angular speed in radians per second?

Accepted Answer

$4.71$ radians/second

Question 10

Which of the following best describes a positive angle in standard position?

Accepted Answer

An angle generated by counterclockwise rotation from the initial side.

Question 11

Find the area of a sector of a circle with radius $6$ feet and central angle $150^{\circ}$. Express your answer in square feet rounded to two decimal places.

Accepted Answer

$47.12$ square feet

Question 12

Which of the following is the correct conversion from $-\frac{7\pi}{4}$ radians to degrees?

Accepted Answer

$-315^{\circ}$

Question 13

If the length of an arc is $10$ cm and the radius of the circle is $5$ cm, what is the measure of the central angle in radians?

Accepted Answer

$2$ radians

Question 14

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

Accepted Answer

They have different initial sides.

Question 15

A point moves on a circle of radius $3$ meters through an angle of $\pi$ radians in $2$ seconds. What is its linear speed?

Accepted Answer

$\frac{3\pi}{2}$ m/s

Question 16

Which of the following angles is NOT an acute angle?

Accepted Answer

$100^{\circ}$

Question 17

What is the formula for the length of a circular arc with radius $r$ and central angle $	heta$ (in radians)?

Accepted Answer

$s = r 	heta$

Question 18

Convert $-300^{\circ}$ to radians.

Accepted Answer

$-\frac{5\pi}{3}$ radians

Question 19

Which of the following is the correct formula for angular speed $\omega$?

Accepted Answer

$\omega = \frac{	heta}{t}$

Question 20

A circle has a radius of $5$ cm. What is the area of a sector formed by a central angle of $60^{\circ}$? Express your answer in square centimeters rounded to two decimal places.

Accepted Answer

$13.09$ cm$^2$

Angles and Radian Measure: Foundations of Trigonometry

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