Geometry Lab reference

Radians & degrees

Two ways to describe the very same turn.

radians = degrees × π / 180

The idea

A radian is the angle that spans an arc equal in length to the radius. A full circle has circumference 2πr, so a full turn is 2π radians. That same turn is 360°.

Work through an example

30° = π/6, 45° = π/4, 60° = π/3, 90° = π/2, and 180° = π. To convert back to degrees, multiply radians by 180/π. For example, 2π/3 radians = 120°.

What to watch for

Check the angle mode when using a calculator. sin(30°) is ½, but sin(30 radians) is a different value. This lab’s triangle inputs use degrees.

Make the formula move.

Explore this idea with real inputs.

See radians on the circle ↗