$$\text{radians} = \text{degrees} \times \frac{\pi}{180}$$

Question 1

Which of the following best describes the initial side and terminal side of an angle in standard position?

Accepted Answer

The initial side is the starting position of the ray, and the terminal side is the position after rotation.

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 $$135^\circ to $$radians.

Accepted Answer

$$\frac{3\pi}{4}$$ radians

Question 4

A circle has a radius of $$8 cm. $$What is the length of the arc intercepted by a central angle of $$60^\circ$$?

Accepted Answer

$$\frac{8\pi}{3} cm$$

Question 5

Which of the following angles is coterminal with $$420^\circ$$?

Accepted Answer

$$60^\circ$$

Question 6

If a hard drive rotates at $$3600$$ revolutions per minute, what is its angular speed in radians per second?

Accepted Answer

$$120\pi$$ radians/sec

Question 7

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

Accepted Answer

$$150^\circ$$

Question 8

A wind turbine blade is $$12$$ feet long and rotates at $$3$$ revolutions per second. What is the linear speed at the tip of the blade?

Accepted Answer

$$72\pi ft/sec$$

Question 9

Which of the following is the correct formula for converting degrees to radians?

Accepted Answer

$$	ext{radians} = 	ext{degrees} 	imes \frac{\pi}{180}$$

Question 10

Find a positive angle less than $$2\pi$$ that is coterminal with $$\frac{17\pi}{6}.$$

Accepted Answer

$$\frac{5\pi}{6}$$

Question 11

A central angle of a circle intercepts an arc of length $$15 cm on a $$circle of radius $$5 cm. $$What is the measure of the angle in radians?

Accepted Answer

$$3$$ radians

Question 12

Which of the following angles is coterminal with $$-120^\circ$$?

Accepted Answer

$$240^\circ$$

Question 13

If $$	heta is in $$standard position and its terminal side coincides with the positive y-axis, what is $$	heta$$?

Accepted Answer

$$90^\circ$$

Question 14

A point moves along a circle of radius $$4$$ meters, sweeping out an angle of $$2$$ radians in $$3$$ seconds. What is its linear speed?

Accepted Answer

$$\frac{8}{3} m/s$$

Question 15

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

Accepted Answer

$$s = r	heta$$

Question 16

Convert $$2.3$$ radians to degrees. (Round to the nearest degree.)

Accepted Answer

$$132^\circ$$

Angles and Radian Measure: Foundations for Trigonometry

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