Q: Which formula is used to find the area 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 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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