Radian Measure

​4.1 Angles and Radian Measures

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Multiple Choice

Convert 150⁰ to radians. #1

MULTIPLY BY (π/180)

• 5π/6

• 3π/4

• 7π/6

• 2π/3

Multiple Choice

Convert 510^o to radians. #9

• 25π / 3

• 23π / 8

• 17π / 6

• 51π / 8

Multiple Choice

Convert π/3 radians to degrees. #2

MULTIPLY BY (180/π).

• 60⁰

• 30⁰

• 90⁰

• 45⁰

Multiple Choice

What is 7π/4 radians in degrees? #3

MULTIPLY BY (180/π)

• 300

• 135

• 315

• 45

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What formula is this? #21

• Arc length when θ is in radians

• Arc length when θ is in degrees

• Sector Area when θ is in radians

• Sector Area when θ is in degrees

Multiple Choice

The length of an arc is 18cm and the radius of the circle is 6cm. What is the radian measure of the central angle? #4

HINT: Use s=θr. PLUG-IN ARC LENGTH AND RADIUS AND SOLVE FOR θ.

• 3 radian

• 2 radian

• 4 radian

• 2π radian

Multiple Choice

A central angle measures 4.5 radians and has an arc of 35 inches. What is the radius of the circle? #5

• 7.78 inches

• 8.21 inches

• 157.5 inches

• 7 inches

Multiple Choice

Find the arc length. #6

Hint: USE S=θr Leave π in the answer.

• 3π/4 ft

• 39π/4 ft

• 13π/4 ft

• 4π/13 ft

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Multiple Choice

Which of the following is closest to the measure of the angle shown? #33

• 7/10 π

• 3/8 π

• 7/20 π

• 3/2 π

Multiple Choice

Which of the following is closest to the measure of the angle drawn by the green curve? #32

• 5/6 π

• 5/3 π

• 4/5 π

• 4/3 π

Multiple Choice

What are the negative and positive coterminal angles of 240 degrees? #34

• 540°, -120°

• 600°, -120°

• 425°, -240°

• 120°, -135°

Multiple Choice

Find a coterminal angle of -180 degrees. #36

• 180

• 90

• 270

• 360

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Multiple Choice

A bicycle wheel with a diameter of .43 m rotates at 3 revolutions per second. What is the linear velocity? (round to tenths) #40

• 8.1 m/s

• 8.2 m/s

• 8.3 m/s

• 8.4 m/s

Multiple Choice

Calculate the angular velocity of a car tire with a radius of .31m traveling at a speed of 22 m/s. #41

• 71 rad/s

• 72 rad/s

• 73 rad/s

• 75 rad/s

Multiple Choice

Determine the linear velocity of the tips of the blades in inches per minute for a ceiling fan with 20-inch blades rotating at 45 rpm. #43

• 5654.9 in/min

• 1800 in/min

• 2827.4 in/min

• 900 in/min