# How do you convert (7, (5pi)/6) into cartesian form?

Feb 11, 2017

The cartesian form is $\left(- \frac{7}{2} \sqrt{3} , \frac{7}{2}\right)$

#### Explanation:

To convert from polar coordinates $\left(r , \theta\right)$ to cartesian coordinates $\left(x , y\right)$, we use the following equations

$x = r \cos \theta$

$y = r \sin \theta$

Therefore,

$x = 7 \cos \left(\frac{5}{6} \pi\right) = - 7 \cdot \frac{\sqrt{3}}{2} = - \frac{7}{2} \sqrt{3}$

$y = 7 \sin \left(\frac{5}{6} \pi\right) = 7 \cdot \frac{1}{2} = \frac{7}{2}$