# How do you find the rectangular coordinate of the following point (5,300)?

Apr 9, 2016

x- coordinate =5 and y- coordinate=300

Apr 9, 2016

If the polar co-ordinates $\left(r , \theta\right) = \left(5 , {300}^{o}\right)$, the rectangular co-ordinates $\left(x , y\right) = \left(\frac{5}{2} , - 5 \frac{\sqrt{3}}{2}\right)$.

#### Explanation:

$x = r \cos \theta \mathmr{and} y = r \sin \theta$.

Here, r = 5 and $\theta = {300}^{o}$.
$\cos {300}^{o} = \cos \left({360}^{o} - {60}^{o}\right) = \cos {60}^{o} = \frac{1}{2}$
$\sin {300}^{o} = \sin \left({360}^{o} - {60}^{o}\right) = - \sin {60}^{o} = - \frac{\sqrt{3}}{2}$.
So, $\left(x , y\right) = \left(\frac{5}{2} , - 5 \frac{\sqrt{3}}{2}\right)$.