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M3-033-A10-V03
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F-TF.1
Warmup
M3-033-A10-V03
Understand radian measure as arc length on the unit circle.
Convert radians to arc length, turns, and degrees
Problem
A circle has radius \(12~\text{units}\) and central rotation \(θ~=~0.5~\text{radians}\). Use the diagram to calculate the arc length, rotation in turns, and degree measure, including the requested exact and approximate forms.
Answer choices
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A
The arc length is 0.5 unit, the rotation is 1/(4pi) turn (about 0.07958 turn), and the degree measure is 90/pi degrees (about 28.6479 degrees).
B
The arc length is 6 units, the rotation is 1/(4pi) turn (about 0.07958 turn), and the degree measure is pi/360 degrees.
C
The arc length is 6 units, the rotation is 1/(4pi) turn (about 0.07958 turn), and the degree measure is 90/pi degrees (about 28.6479 degrees).
D
The arc length is 12pi units, the rotation is 1/(4pi) turn (about 0.07958 turn), and the degree measure is 90/pi degrees (about 28.6479 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
