A circle is intimately related to angles. Everyone knows as you swing from 0 degrees all the way around to 360 degrees, you make a circle. The points on our unit circle figure show angles. Up above we drew bigger and bigger angles moving around the circle.
People talk about angles several different ways. If you’ve ever noticed the DRG button on a calculator, that stands for DEGREES RADIANS GRADIANS, which are three different ways to refer to angles. Our unit circle figure shows both degrees and radians. Radians are based on the how long the curvy part of a unit circle is that the angle hits. When you run all the way around 360 degrees, the curvy part is the whole circumference or 2π times the radius. So 360 degrees is 2π radians. At 90 degrees you get a quarter of that curvy part, so 90 degrees is π/2 radians.

A circle is intimately related to angles. Everyone knows as you swing from 0 degrees all the way around to 360 degrees, you make a circle. The points on our unit circle figure show angles. Up above we drew bigger and bigger angles moving around the circle.

People talk about angles several different ways. If you’ve ever noticed the DRG button on a calculator, that stands for DEGREES RADIANS GRADIANS, which are three different ways to refer to angles. Our unit circle figure shows both degrees and radians. Radians are based on the how long the curvy part of a unit circle is that the angle hits. When you run all the way around 360 degrees, the curvy part is the whole circumference or 2π times the radius. So 360 degrees is 2π radians. At 90 degrees you get a quarter of that curvy part, so 90 degrees is π/2 radians.