# Radians of the unit circle.

• Nov 2nd 2012, 10:21 AM
Eraser147
For the radians of the unit circle that are degree 30, 45, and 60.. is there a way where I can find the radians without using a calculator by converting degree to radians? Like for example why is 60 degrees on the unit circle pi over 3. What is the formula for adding up the radians throughout the whole unit circle?
• Nov 2nd 2012, 10:50 AM
HallsofIvy
Re: Radians of the unit circle.
You just need to know: 1) the relation ship is linear, 2) 0 degrees= 0 radians, 3) 360 degrees= $2\pi$ radians
$\frac{x degrees}{y radians}= \frac{360}{2\pi}$.

So if "x degrees" is "30 degrees" we have $\frac{30 degrees}{y radians}= \frac{360}{2\pi}$. Now "cross multiply": $(y radians)(360)= (30 degrees)(2\pi)= 60\pi$. $y radians= \frac{60\pi}{360}= \frac{\pi}{6} radians$.
• Nov 2nd 2012, 10:56 AM
Plato
Re: Radians of the unit circle.
Quote:

Originally Posted by Eraser147
For the radians of the unit circle that are degree 30, 45, and 60.. is there a way where I can find the radians without using a calculator by converting degree to radians? Like for example why is 60 degrees on the unit circle pi over 3. What is the formula for adding up the radians throughout the whole unit circle?

Think in terms of units, like feet, yards, meters etc.
$(N\deg)\left(\frac{\pi}{180\deg}\right)=\left( \frac{N\pi}{180}\right)$

$(N^o)\left(\frac{\pi}{180^o}\right)=\left( \frac{3\pi}{4}\right)$