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.