# What is the Cartesian form of (100,(17pi)/16))?

Dec 25, 2015

The given point is in polar coordinates $\left(r , \theta\right)$ form and the cartesian coordinates are obtained by $\left(r \cos \left(\theta\right) , r \sin \left(\theta\right)\right)$ The working is given below.

#### Explanation:

$\left(100 , \frac{17 \pi}{16}\right)$
$r = 100$ and $\theta = \frac{17 \pi}{16}$

$x = r \cos \left(\theta\right)$ and $y = r \sin \left(\theta\right)$

$x = 100 \cos \left(\frac{17 \pi}{16}\right)$ and $y = 100 \sin \left(\frac{17 \pi}{16}\right)$

The cartesian form is

$\left(100 \cos \left(\frac{17 \pi}{16}\right) , 100 \sin \left(\frac{17 \pi}{16}\right)\right)$

We can find approximate value using calculator and that works out to be

$\left(- 98.0785 , - 19.5090\right)$ Answer