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

Mar 26, 2017

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

#### Explanation:

To find the Cartesian form of polar coordinates (i.e. the $x$ and $y$ coordinates), use the following formulas:

$x = r \cos \theta$
$y = r \sin \theta$

In this case, $r = 1$ and $\theta = \frac{\pi}{4}$.

So, just plug in these values to get your coordinates.

$x = 1 \cdot \cos \left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}$
$y = 1 \cdot \sin \left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}$

Therefore, the Cartesian form of $\left(1 , \frac{\pi}{4}\right)$ is $\left(\frac{\sqrt{2}}{2} , \frac{\sqrt{2}}{2}\right)$.