# What is the Cartesian form of (9,(3pi )/4)?

The Cartesian form of $\left(r , \theta\right) = \left(9 , \frac{3 \pi}{4}\right)$ is $\left(x , y\right) = \left(- \frac{9 \sqrt{2}}{2} , \frac{9 \sqrt{2}}{2}\right)$.
Use the equations $x = r \cos \left(\theta\right)$ and $y = r \sin \left(\theta\right)$ to get $x = 9 \cos \left(\frac{3 \pi}{4}\right) = 9 \cdot - \frac{\sqrt{2}}{2} = - \frac{9 \sqrt{2}}{2}$ and $y = 9 \sin \left(\frac{3 \pi}{4}\right) = 9 \cdot \frac{\sqrt{2}}{2} = \frac{9 \sqrt{2}}{2}$.