Radian Measure of an Angle
Big Idea: Degrees aren't the only way to measure angles! Radians provide a natural, elegant way to measure angles based on the geometry of a circle itself.
1. What is a Radian?
Definition: A radian is the measure of a central angle that intercepts an arc whose length is equal to the radius of the circle.
Imagine you take the radius of a circle and "wrap" it along the circumference. The angle formed at the center by that arc is exactly 1 radian.
$$ \theta = \frac{s}{r} $$
where $\theta$ is the angle in radians, $s$ is the arc length, and $r$ is the radius.