# How do you convert (2,(-7pi)/6) into cartesian form?

May 10, 2017

Use $x = r \cos \theta$ and $y = r \sin \theta$. Answer: $\left(- \sqrt{3} , 1\right)$

#### Explanation:

Original problem: Convert $\left(2 , - \frac{7 \pi}{6}\right)$ to Cartesian

To convert from polar coordinates to Cartesian form, we use the equations $x = r \cos \theta$ and $y = r \sin \theta$.

Since we have $\left(r , \theta\right)$, we can simply substitute into the above formulas:
$x = 2 \cos \left(- \frac{7 \pi}{6}\right)$
Using our unit circle trig values
$x = 2 \left(- \frac{\sqrt{3}}{2}\right)$
$x = - \sqrt{3}$

$y = 2 \sin \left(- \frac{7 \pi}{6}\right)$
Using our unit circle trig values
$y = 2 \left(\frac{1}{2}\right)$
$y = 1$

Therefore our final answer in Cartesian form is: $\left(- \sqrt{3} , 1\right)$