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 quadrantal angle?

Accepted Answer

An angle in standard position with its terminal side along the x- or y-axis.

Question 2

If two angles are supplementary, what is the sum of their measures?

Accepted Answer

$$180^\circ$$

Question 3

Convert $$120^\circ to $$radians.

Accepted Answer

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

Question 4

A circle has a radius of 10 cm. What is the length of the arc intercepted by a central angle of $$\frac{\pi}{2}$$ radians?

Accepted Answer

$$5\pi cm$$

Question 5

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 6

A belt runs a pulley of radius 6 cm at 80 revolutions per minute. What is the angular speed of the pulley in radians per second?

Accepted Answer

$$\frac{8\pi}{3}$$ radians per second

Question 7

Which of the following is a coterminal angle to $$-75^\circ$$?

Accepted Answer

$$285^\circ$$

Question 8

Convert $$2.5$$ radians to degrees.

Accepted Answer

$$143.2^\circ$$

Question 9

The latitude of City A is $$52^\circ N $$and City B is $$40^\circ N. If $$the radius of Earth is $$6400 km$$, what is the north-south distance between the two cities?

Accepted Answer

$$1340 km$$

Question 10

A point $$P is on a $$circle of radius $$10 cm$$, and ray $$OP$$ rotates with angular speed $$\frac{\pi}{18}$$ radians per second. What is the linear speed of $$P$$?

Accepted Answer

$$\frac{5\pi}{9} cm/s$$

Question 11

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

Accepted Answer

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

Question 12

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

Accepted Answer

$$1$$ radian

Question 13

Convert $$74^\circ 8' 14'' to $$decimal degrees.

Accepted Answer

$$74.137^\circ$$

Question 14

Which of the following is NOT a property of a straight angle?

Accepted Answer

It is an obtuse angle.

Question 15

A sector of a circle has a radius of $$5 m $$and a central angle of $$2$$ radians. What is its area?

Accepted Answer

$$25 m$^2$$

Question 16

Which of the following is the correct formula for arc length $$s$$?

Accepted Answer

$$s = r	heta$$

Question 17

If the sum of two angles is $$90^\circ$$, what are they called?

Accepted Answer

Complementary

Question 18

Which of the following is the correct conversion factor to change degrees to radians?

Accepted Answer

$$\frac{\pi}{180}$$

Question 19

A central angle of $$144^\circ$$ intercepts an arc on a circle of radius $$18.2 cm. $$What is the arc length?

Accepted Answer

$$45.74 cm$$

Question 20

Which of the following is true about coterminal angles?

Accepted Answer

Their measures differ by a multiple of $$360^\circ.$$

Angles, Arc, and Their Measures – Trigonometry Foundations

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