Question

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

Answer 1

`(-4, 0)`

Explanation:

Given polar coordinates `(4, 3\pi)\equiv(r, \theta)`

hence, the cartesian coordinates `(x, y)` are given as follows

`x=r\cos\theta=4\cos(3\pi)=4(-1)=-4`

`y=r\sin\theta=4\sin(3\pi)=4(0)=0`

`\therefore (x, y)\equiv(-4, 0)`

Answer 2

`(4,0)`

Explanation:

`(4,0)`

Given polar coordinates `(-4, 3\pi)\equiv(r, \theta)`

hence, the cartesian coordinates `(x, y)` are given as follows

`x=r\cos\theta=-4\cos(3\pi)=-4(-1)=4`

`y=r\sin\theta=-4\sin(3\pi)=-4(0)=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 `3pi` 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)

For more info: https://www.dummies.com/education/math/calculus/how-to-graph-polar-coordinates-with-negative-values/