# How do I convert polar coordinates (-4, 230^circ) to rectangular coordinates?

Sep 30, 2014

$\left(r , \theta\right) \to \left(- 4 , 230\right)$

${230}^{\circ}$ has to be converted to radians.

${230}^{\circ} \cdot \frac{\pi}{180} ^ \circ = \frac{230 \pi}{180} = \frac{23 \pi}{18}$
$x = r \cos \left(\theta\right) = \left(- 4\right) \cdot \cos \left(\frac{23 \pi}{18}\right) = - 4 \left(- 0.6428\right) = 2.5712$
$y = r \sin \left(\theta\right) = \left(- 4\right) \cdot \sin \left(\frac{23 \pi}{18}\right) = - 4 \left(- 0.7660\right) = 3.0641$
$\left(r , \theta\right) \to \left(- 4 , 230\right)$
$\left(x , y\right) \to \left(2.5712 , 3.0641\right)$