# What is the Cartesian form of ( 4 , ( 11pi)/4 ) ?

Mar 22, 2016

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

#### Explanation:

Using the formulae that links Polar to Cartesian coordinates.

• x = rcostheta

• y = rsintheta

here r = 4 and $\theta = \frac{11 \pi}{4}$
$\text{---------------------------------------------------}$
$\Rightarrow x = 4 \cos \left(\frac{11 \pi}{4}\right) = 4 \cos \left(\frac{11 \pi}{4} - 2 \pi\right) = \cos \left(\frac{3 \pi}{4}\right)$

and $\cos \left(\frac{3 \pi}{4}\right) = - \cos \left(\frac{\pi}{4}\right) = - \frac{1}{\sqrt{2}}$
thus $x = 4 \times \frac{- 1}{\sqrt{2}} = - 2 \sqrt{2}$
$\text{-------------------------------------------------}$

$\Rightarrow y = 4 \sin \left(\frac{11 \pi}{4}\right) = 4 \sin \left(\frac{\pi}{4}\right) = 4 \times \frac{1}{\sqrt{2}} = 2 \sqrt{2}$