Explore radian measure by following these steps.

✓ 1. Move point K to set m∠JPK to 1 radian. For both circles, what is the relationship between the arc length and radius? arc length < radius arc length = radius arc length > radius

✓ 2. Move point K to set m∠JPK to 2 radians. For both circles, what is the relationship between the arc length and radius? arc length = radius arc length = 2 × radius arc length = radius − 2

✓ 3. Because all circles are similar, for any circle with radius r and arc length s, there is a constant of proportionality k, such that
r = k × 1.

It is also true that for any central angle θ, s = k × 1 π θ.

✓ 4. Therefore by substitution, s = k rπ rθ .