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

Jun 14, 2016

$\therefore \left(x , y\right) = \left(- 7 \frac{\sqrt{3}}{2} , \frac{7}{2}\right) .$

#### Explanation:

Let $\left(r , \theta\right)$ be the given polar co-ords. & let $\left(x , y\right)$ be their Cartesian conversion.

Then, we know that $x = r \cos \theta , y = r \sin \theta .$

Hence, with $r = 7 , \theta = 5 \frac{\pi}{6} ,$ we get, $x = 7 \cos 5 \frac{\pi}{6} , y = 7 \sin 5 \frac{\pi}{6.}$

$\therefore x = 7 \cos \left(\pi - \frac{\pi}{6}\right) , y = 7 \sin \left(\pi - \frac{\pi}{6}\right) .$

$\therefore x = 7 \left(- \cos \left(\frac{\pi}{6}\right)\right) , y = 7 \sin \left(\frac{\pi}{6}\right) .$

$\therefore x = - 7 \frac{\sqrt{3}}{2} , y = \frac{7}{2}$
$\therefore \left(x , y\right) = \left(- 7 \frac{\sqrt{3}}{2} , \frac{7}{2}\right) .$