# What is the Cartesian form of ( 12 , (23pi)/3 ) ?

Dec 27, 2016

$\left(6 , - 10.4\right)$

#### Explanation:

in polar forms, the first coordinate is always the hypotenuse.

$r = 12$

$\theta = \frac{23 \pi}{3}$

$x$ and $y$ can be solved as the adjacent and opposite, respectively.

using $\sin$ and $\cos$ ratios:

$\sin \frac{23 \pi}{3} = \frac{O}{H} = \frac{y}{12}$

$y = 12 \cdot \sin \left(\frac{23 \pi}{3}\right)$

$= - 10.4 \left(3 s . f .\right)$

$\cos \frac{23 \pi}{3} = \frac{A}{H} = \frac{x}{12}$

$x = 12 \cdot \cos \frac{23 \pi}{3}$

$= 6$

cartesian coordinates: $\left(6 , - 10.4\right)$