How do you convert ( 6, pi/ 6)  into cartesian form?

Dec 30, 2016

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

Explanation:

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

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

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder}}$

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

$\text{here " r=6" and } \theta = \frac{\pi}{6}$

$\Rightarrow x = 6 \cos \left(\frac{\pi}{6}\right) = 6 \times \frac{\sqrt{3}}{2} = 3 \sqrt{3}$

$\text{and } y = 6 \sin \left(\frac{\pi}{6}\right) = 6 \times \frac{1}{2} = 3$

$\Rightarrow \left(6 , \frac{\pi}{6}\right) \to \left(3 \sqrt{3} , 3\right)$