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

2 Answers

(-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)

Jul 1, 2018

(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/