# How do you find the rectangular coordinate of (1, 45 degrees)?

Jun 22, 2018

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

#### Explanation:

the Polar coordinate

$\left(1 , {45}^{0}\right) = \left(r , \theta\right)$

now

$x = r \cos \theta$

$y = r \sin \theta$

$\therefore x = 1 \times \cos 45 = \frac{\sqrt{2}}{2}$

$y = 1 \times \sin 45 = \frac{\sqrt{2}}{2}$

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