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

Nov 1, 2016

Cartesian form:$\left(\textcolor{b l u e}{12 , 0}\right)$

#### Explanation:

The Cartesian form$\left(x , y\right)$ of the polar coordinates $\left(12 , \frac{12 \pi}{3}\right)$

$\textcolor{b l u e}{x = r \cos \theta} = 12 \times \cos \left(\frac{12 \pi}{3}\right) = 12 \times \cos \left(4 \pi\right) = 12 \times 1$
color(blue)(x=12

$\textcolor{b l u e}{y = r \sin \theta} = 12 \times \sin \left(\frac{12 \pi}{3}\right) = 12 \times \sin \left(4 \pi\right) = 12 \times 0$
color(blue)(y=0

Cartesian form of polar coordinates $\left(12 , \frac{12 \pi}{3}\right)$ is $\left(\textcolor{b l u e}{12 , 0}\right)$