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M3-033-A10-V04
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F-TF.1
Warmup
M3-033-A10-V04
Understand radian measure as arc length on the unit circle.
Convert radians to arc length, turns, and degrees
Problem
A circle has radius \(1~\text{unit}\) and central rotation \(θ~=~3~\text{radians}\). Use the diagram to calculate the arc length, rotation in turns, and degree measure, including the requested exact and approximate forms.
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A
The arc length is 6 units, the rotation is 3/(2pi) turn (about 0.47746 turn), and the degree measure is 540/pi degrees (about 171.8873 degrees).
B
The arc length is 6pi units, the rotation is 3/(2pi) turn (about 0.47746 turn), and the degree measure is 540/pi degrees (about 171.8873 degrees).
C
The arc length is 3 units, the rotation is 3/(2pi) turn (about 0.47746 turn), and the degree measure is 540/pi degrees (about 171.8873 degrees).
D
The arc length is 3 units, the rotation is 3/(2pi) turn (about 0.47746 turn), and the degree measure is pi/60 degrees.
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Curriculum context
Standard F-TF.1
Category Functions
Domain Trigonometric Functions
Objective Understand radian measure as arc length on the unit circle.
Problem type Convert radians to arc length, turns, and degrees
