# 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]]