# What is the Cartesian form of (-2,(88pi) /16)?

Sep 8, 2016

Polar $\left(r , \theta\right) = \left(- 2 , \frac{88 \pi}{16}\right)$ is equivalent to Cartesian $\left(x , y\right) = \left(0 , 2\right)$

#### Explanation:

$\theta = \frac{88 \pi}{16} = 5 \pi + \frac{\pi}{2}$
Since $2 \pi$ makes one full circle
$\frac{88 \pi}{16}$ is equivalent to $\frac{3 \pi}{2}$

As an angle $\frac{3 \pi}{2}$ maps on to the negative Y-axis in the Cartesian system.

The polar point $\left(- 2 , \frac{88 \pi}{16}\right)$ is therefore a distance of $\left(- 2\right)$ from the origin measured down the negative Y-axis;
but $\left(- 2\right)$ down the negative Y-axis is the same as $+ 2$ up the positive Y-axis.

Therefore $\left(- 2 , \frac{88 \pi}{16}\right)$ is a point on the Y-axis at $y = 2$;
that is at $\left(x , y\right) = \left(0 , 2\right)$