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### 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 $$\pi$$.