# What is the Cartesian equivalent of polar coordinates (7, pi)?

Oct 1, 2014

In this problems we know that $\left(r , \theta\right) \to \left(7 , \pi\right)$.

We also know the following equations are used to convert polar coordinates to rectangular coordinates.

$\left(x , y\right) \to \left(r \cos \left(\theta\right) , r \sin \left(\theta\right)\right)$

Substitute in the values for $r$ and $\theta$

$\left(x , y\right) \to \left(7 \cos \left(\pi\right) , 7 \sin \left(\pi\right)\right)$

Remember back to the unit circle

$\cos \left(\pi\right) = - 1$
$\sin \left(\pi\right) = 0$

Substitute in those values

$\left(x , y\right) \to \left(7 \left(- 1\right) , 7 \left(0\right)\right)$

Simplify

$\left(x , y\right) \to \left(- 7 , 0\right)$