Question 1

Which of the following best describes an angle in standard position?

Accepted Answer

Its vertex is at the origin and its initial side lies along the positive x-axis.

Question 2

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

Accepted Answer

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

Question 3

A central angle in a circle of radius 10 cm intercepts an arc of length 15 cm. What is the measure of the angle in radians?

Accepted Answer

$$1.5$$

Question 4

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

Accepted Answer

$$315^\circ$$

Question 5

If an object moves along a circular path of radius 4 meters and sweeps out a central angle of $$\frac{\pi}{2}$$ radians, what is the length of the arc traveled?

Accepted Answer

$$2\pi$$ meters

Question 6

Convert $$\frac{5\pi}{6}$$ radians to degrees.

Accepted Answer

$$150^\circ$$

Question 7

A wheel rotates at an angular speed of $$3$$ radians per second. If the radius of the wheel is $$0.5$$ meters, what is the linear speed at the rim?

Accepted Answer

$$1.5$$ meters/second

Question 8

Which of the following is the correct formula for the length of a circular arc?

Accepted Answer

$$s = r	heta$$

Question 9

A Ferris wheel makes one complete revolution in 40 seconds. What is the angular speed in radians per second?

Accepted Answer

Question 10

Which of the following statements is true about coterminal angles?

Accepted Answer

Coterminal angles have the same initial and terminal sides but may have different measures.

Question 11

A runner completes a lap around a circular track of radius 50 meters, running a total distance equal to the circumference. What is the central angle in radians corresponding to one lap?

Accepted Answer

$$2\pi$$

Question 12

Convert $$-210^\circ to $$radians.

Accepted Answer

$$-\frac{7\pi}{6}$$

Question 13

If a car tire with a radius of 0.3 meters rotates through an angle of $$4\pi$$ radians, what distance does a point on the edge of the tire travel?

Accepted Answer

$$1.2\pi$$ meters

Question 14

Which of the following is NOT a correct way to describe a right angle?

Accepted Answer

$$180^\circ$$

Question 15

A clock’s minute hand is 12 cm long. How far does the tip of the minute hand travel in 20 minutes?

Accepted Answer

$$16\pi cm$$

Question 16

Which of the following best describes a straight angle?

Accepted Answer

$$180^\circ$$

Question 17

If an angle measures $$\frac{3\pi}{4}$$ radians, what is its degree measure?

Accepted Answer

$$135^\circ$$

Question 18

A gear rotates at $$2$$ revolutions per second. What is its angular speed in radians per second?

Accepted Answer

$$4\pi$$

Question 19

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

Accepted Answer

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

Question 20

A central angle of $$\frac{\pi}{3}$$ radians in a circle of radius 6 meters intercepts an arc. What is the length of the arc?

Accepted Answer

$$2\pi$$ meters

Angles and Radian Measure – Foundations of Trigonometric Functions

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