Question

How do you convert $-220$ degrees to radians without a calculator?

Answer 1

Convert degrees to radians.

$1°=\left(\frac{\mathrm{\pi }}{180}\right)\mathrm{radians}$

Mutiply both sides by $-220$.

$\begin{array}{rcl}-220°& =& -220\times \left(\frac{\mathrm{\pi }}{180}\right)\mathrm{radians}\\ & =& -\frac{11\mathrm{\pi }}{9}\mathrm{radians}\end{array}$

Hence, $\mathbf{-}\mathbf{220}$ degree is written as $\mathbf{-}\frac{\mathbf{11}\mathbf{\pi }}{\mathbf{9}}$ radians.