What is the Cartesian form of ( 6 , ( 9pi)/4 ) ?

1 Answer
Oct 18, 2016

$\left(3 \sqrt{2} , 3 \sqrt{2}\right)$

Explanation:

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

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 = 6 and $\theta = \frac{9 \pi}{4}$

$\Rightarrow x = 6 \cos \left(\frac{9 \pi}{4}\right) = 6 \cos \left(\frac{9 \pi}{4} - 2 \pi\right)$

$= 6 \cos \left(\frac{\pi}{4}\right) = 6 \times \frac{1}{\sqrt{2}} = \frac{6 \sqrt{2}}{2} = 3 \sqrt{2}$

and $y = 6 \sin \left(\frac{9 \pi}{4}\right) = 6 \sin \left(\frac{9 \pi}{4} - 2 \pi\right)$

$= 6 \sin \left(\frac{\pi}{4}\right) = 6 \times \frac{1}{\sqrt{2}} = 3 \sqrt{2}$

$\Rightarrow \left(6 , \frac{9 \pi}{4}\right) \to \left(3 \sqrt{2} , 3 \sqrt{2}\right)$