Find the rectangular coordinates of the point that has polar

Find the rectangular coordinates of the point that has polar coordinates (-3, 2 pi / 3).

Solution

The equations for converting rectangular coordinates to polar coordinates are:
x = r * cos() and y = r * sin().

In the polar coordinates given r = -3, and = 2/3.

Filling in the terms we get x = -3 cos(2/3) and y = -3 sin (2/3). We know that cos(2/3) = -1/2 and sin(2/3) = 3/2.

Thus, x = -3/2 and y = -(33)/2