# Radians
A radian is the angle formed when the radius is the distance around the circle from the initial side to the terminal side.
The circumference of a circle can be measured 2 times $\pi$ times the length of the radius.
$2\pi r = 360\degree$
![[Pasted image 20240721195858.jpg]]
- 1 rotation $= 360\degree = 2\pi ~radians$
- $\frac{1}{2}$ rotation $= 180\degree = \pi ~radians$
- $\frac{1}{4}$ rotation $= 90\degree = \frac{\pi}{2} ~radians$
- 1$\degree$ = $\frac{\pi}{180}$
## Converting Radians and Degrees.
$\frac{Degrees}{360} = \frac{Radians}{2\pi}$
$1\degree=\frac{\pi}{180}$
$1~Radian=\frac{180\degree}{\pi}$
$Degrees = Radians * \frac{180\degree}{\pi}$
$Radians = Degrees * \frac{\pi}{180}$
![[Pasted image 20240721193318.jpg]]