# How do you find the rectangular coordinate of (sqrt 2, 315 degrees)?

Jan 21, 2016

( 1 , -1 )

#### Explanation:

To convert from Polar to Rectangular coordinates use :

• x = rcostheta | y = rsintheta

Here $r = \sqrt{2} , \theta = {315}^{\circ}$

$\Rightarrow x = \sqrt{2} \cos {315}^{\circ} , y = \sqrt{2} \sin {315}^{\circ}$

Note : $\cos {315}^{\circ} = \cos {45}^{\circ}$

and $\sin {315}^{\circ} = - \sin {45}^{\circ}$

The 'exact value of $\cos {45}^{\circ} = \frac{1}{\sqrt{2}}$
The 'exact value' of $\sin {45}^{\circ} = \frac{1}{\sqrt{2}}$

$\Rightarrow x = \sqrt{2} \cos {45}^{\circ} = \sqrt{2} \times \frac{1}{\sqrt{2}} = 1$

and y $= \sqrt{2} \left(- \sin {45}^{\circ}\right) = \sqrt{2} \times - \left(\frac{1}{\sqrt{2}}\right) = - 1$

$\Rightarrow \left(\sqrt{2} , {315}^{\circ}\right) = \left(1 , - 1\right)$