# How do you convert (-4, 3pi) from polar to cartesian coordinates?

$\left(- 4 , 0\right)$

#### Explanation:

Given polar coordinates $\left(4 , 3 \setminus \pi\right) \setminus \equiv \left(r , \setminus \theta\right)$

hence, the cartesian coordinates $\left(x , y\right)$ are given as follows

$x = r \setminus \cos \setminus \theta = 4 \setminus \cos \left(3 \setminus \pi\right) = 4 \left(- 1\right) = - 4$

$y = r \setminus \sin \setminus \theta = 4 \setminus \sin \left(3 \setminus \pi\right) = 4 \left(0\right) = 0$

$\setminus \therefore \left(x , y\right) \setminus \equiv \left(- 4 , 0\right)$

Jul 1, 2018

$\left(4 , 0\right)$

#### Explanation:

$\left(4 , 0\right)$

Given polar coordinates $\left(- 4 , 3 \setminus \pi\right) \setminus \equiv \left(r , \setminus \theta\right)$

hence, the cartesian coordinates $\left(x , y\right)$ are given as follows

$x = r \setminus \cos \setminus \theta = - 4 \setminus \cos \left(3 \setminus \pi\right) = - 4 \left(- 1\right) = 4$

$y = r \setminus \sin \setminus \theta = - 4 \setminus \sin \left(3 \setminus \pi\right) = - 4 \left(0\right) = 0$

The $- r$ can essentially be seen as a reflection, so if you were to plot this by hand on a polar graph.

You would go to the angle $3 \pi$ which is essentially just $\pi$ as they are co-terminal, you would move out 4 units from the center at r=4, and you would reflect across the y-axis because the r is negative, so you would end up at (4,0)