# What is the Cartesian form of (2,(pi )/3)?

Oct 31, 2016

$\left(1 , \sqrt{3}\right)$

#### Explanation:

To convert from $\textcolor{b l u e}{\text{polar to cartesian coordinates}}$

That is $\left(r , \theta\right) \to \left(x , y\right)$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder }} \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{x = r \cos \theta , y = r \sin \theta} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

here $r = 2 \text{ and } \theta = \frac{\pi}{3}$

$\Rightarrow x = 2 \cos \left(\frac{\pi}{3}\right) = 2 \times \frac{1}{2} = 1$

and $y = 2 \sin \left(\frac{\pi}{3}\right) = 2 \times \frac{\sqrt{3}}{2} = \sqrt{3}$

$\Rightarrow \left(2 , \frac{\pi}{3}\right) \to \left(1 , \sqrt{3}\right)$