# What is the Cartesian form of (1,(-pi )/4)?

Jul 21, 2017

$\left(\frac{1}{\sqrt{2}} , - \frac{1}{\sqrt{2}}\right)$

#### Explanation:

We're asked to find the Cartesian (rectangular) form of a polar coordinate.

We can use two simple equations to get the $x$- and $y$-coordinates:

$x = r \cos \theta$

$y = r \sin \theta$

Here.

• $r = 1$

• $\theta = - \frac{\pi}{4}$

So we have

x = (1)cos(-pi/4) = color(red)(1/sqrt2

y = (1)sin(-pi/4) = color(blue)(-1/sqrt2

The Cartesian form is thus

$\left(\textcolor{red}{\frac{1}{\sqrt{2}}} , \textcolor{b l u e}{- \frac{1}{\sqrt{2}}}\right)$