Contact The Learning Centre
Radian Measure
Converting between degrees and radians
- To convert from radians to degrees, find the angle as a fraction of the full circle (\(2\pi\)) then multiply by \(360^{\circ}\):
\[ \mbox{Number of Degrees} = \frac{\mbox{Number of radians}}{2\pi}\times 360^{\circ}\]
- For example: convert \(\displaystyle \frac{7\pi}{8} \) radians to degrees:
\begin{eqnarray*}
\mbox{Number of Degrees} &=& \frac{\mbox{Number of radians}}{2\pi}\times 360^{\circ} \\
&=& \frac{\frac{7\pi}{8}}{2\pi}\times 360^{\circ} \\
&=& 157.5^{\circ}
\end{eqnarray*}
- To convert degrees to radians, find the angle as a fraction of the full circle (\(360^{\circ}\)) then multiply by \(2\pi\):
\[ \mbox{Number of Radians} = \frac{\mbox{Number of Degrees}}{360^{\circ}}\times 2\pi\]
- For example: convert \(135^{\circ}\) to radians:
\begin{eqnarray*}
\mbox{Number of Radians} &=& \frac{\mbox{Number of Degrees}}{360^{\circ}}\times 2\pi \\
&=& \frac{135^{\circ}}{360^{\circ}}\times 2\pi \\
&=& \frac{3\pi}{4}
\end{eqnarray*}
- Note that when possible we try to leave radians as a fraction of \(\pi\).