Problem preview
F-TF.1 Warmup M3-033-A03-V01

Understand radian measure as arc length on the unit circle.

Find arc length from a radius and a central angle measured in radians

Problem

What is the arc length when the radius is \(4\) and the angle is \(\pi/3~\text{radians}\)?

Big Picture

What this problem is really about

When the angle is already in radians, arc length scales directly as radius times angle measure. Preserve an exact pi fraction instead of converting it, since it also reveals what fraction of a full turn the angle represents. The same fraction of the full circumference gives an independent check on the arc length.

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Four variants of this problem type
Curriculum context
Course
Math III
Standard
F-TF.1
Category
Functions
Domain
Trigonometric Functions
Objective
Understand radian measure as arc length on the unit circle.
Problem type
Find arc length from a radius and a central angle measured in radians