If the arc length of a sector in the unit circle is 3 radians, what is the measure of the angle of the sector? a) 1.5 radians b) 3 radians c) 6 radians d) 9 radians

B) 3 radians

Step-by-step explanation:

The arc length is the product of the radius and angle. You have ...

... 3 radians = 1 × angle

so

... 3 radians = angle

Comment on units

The formula is

... s = rθ . . . . . where s is the arc length, r is the radius, and θ is the central angle in radians.

The units of both s and r are units of length, so the units of angle are ...

... (length units)/(length units) = <no units>

That is, "radians" are fully equivalent to "no units."

The trouble with this problem statement is that it expresses "arc length" in units of "radians." This only works if the units of the radius of the unit circle are "no units". Ordinarily, that would not be the case. The length of the radius of the unit circle is usually "one length unit." If the central angle is 3 radians, then the arc length is "3 length units," not "3 radians."

step-by-step explanation:

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