# What is the Cartesian form of ( 8 , (13pi)/6 ) ?

Cartesian form of $\left(8 , \frac{13 \pi}{6}\right)$is$= \left(4 \sqrt{3} , 4\right)$

#### Explanation:

Given $r = 8$
$\theta = \frac{13 \pi}{6}$
Formulas;
$x = r \cdot \cos \theta$ and $y = r \cdot \sin \theta$

Solve for the Cartesian coordinates:
For x:
$x = r \cos \theta$
$x = 8 \cdot \cos \left(\frac{13 \pi}{6}\right)$
$x = 4 \sqrt{3}$

For y:
$y = r \sin \theta$
$y = 8 \cdot \sin \left(\frac{13 \pi}{6}\right)$
$y = 8 \cdot \left(\frac{1}{2}\right)$
$y = 4$

Final answer $\left(4 \sqrt{3} , 4\right)$