Problem preview
F-TF.1 Warmup M3-033-A01-V01

Understand radian measure as arc length on the unit circle.

Define one radian with the arc-length ratio

Problem

Use the diagram to define \(\text{one}~\text{radian}\) by relating intercepted arc length \(s\), radius \(r\), and central angle \(θ\).

Big Picture

What this problem is really about

Radian measure compares two lengths on the same circle: distance along the intercepted arc divided by the radius. That ratio tells how many radius-lengths fit along the arc, so equal arc and radius lengths define the unit benchmark. The curved arc matters here, not the straight chord between its endpoints.

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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
Define one radian with the arc-length ratio