# What is the Cartesian form of ( -9 , ( - 15pi)/2 ) ?

Jul 26, 2018

(0. -9)

#### Explanation:

We have the coordinate $\left(- 9 , \frac{- 15 \pi}{2}\right)$ in polar form.

Coordinates in polar form have the standard form (color(green)(r), color(purple)(Θ)).

To convert from polar form to Cartesian form, we use the following formulas:

• color(red)(x) = color(green)(r)coscolor(purple)(Θ)
• color(blue)(y) = color(green)(r)sincolor(purple)(Θ)

Now, let's plug stuff in. We know $\textcolor{g r e e n}{r} = - 9$ and color(purple)(Θ) = (-15pi)/2

$\textcolor{red}{x} = \left(- 9\right) \cdot \cos \left(\frac{- 15 \pi}{2}\right)$

$\textcolor{red}{x} = \left(- 9\right) \cdot \left(0\right)$

$\textcolor{red}{x} = 0$

$\textcolor{b l u e}{y} = \left(- 9\right) \cdot \sin \left(\frac{- 15 \pi}{2}\right)$

$\textcolor{b l u e}{y} = \left(- 9\right) \cdot \left(1\right)$

$\textcolor{b l u e}{y} = - 9$

We get $\textcolor{red}{x} = 0$ and $\textcolor{b l u e}{y} = - 9$, making our Cartesian coordinate $\left(0 , - 9\right) .$