Problem preview
F-TF.1 Warmup M3-033-A09-V01

Understand radian measure as arc length on the unit circle.

Find a missing arc length or angle measure using radians

Problem

A wheel with radius \(3~\text{ft}\) rotates through \(4~\text{radians}\). How far does a point on the rim travel along the arc?

Big Picture

What this problem is really about

A radian angle tells how many radius-lengths are swept along a circle, so multiplying the radius by the angle gives the traveled arc distance. Keep the angle unit distinct from the requested linear unit. Comparing the rotation with a full turn and the distance with the full circumference provides a useful scale check.

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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 a missing arc length or angle measure using radians