# What is the Cartesian form of (-27,(-9pi)/6))?

Dec 20, 2016

Polar: $\left(r , \theta\right) = \left(- 27 , \frac{- 9 \pi}{6}\right)$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow$Cartesian: $\left(x , y\right) = \left(0 , - 27\right)$

#### Explanation:

Note that an angle of $\frac{- 9 \pi}{6}$ is equivalent to an angle of $\frac{3 \pi}{6} = \frac{\pi}{2}$

This tells us that the point is on the Y-axis (i.e. the $x$ coordinate value is $0$)

Since the radius is given as $\left(- 27\right)$ the point is $27$ units down the Y-axis from the origin (i.e. at $y = - 27$)