Find polar coordinates of the point that has rectangular coo

Find polar coordinates of the point that has rectangular coordinates(4 squareroot 3, -4). Write your answer using degree.

Solution

We know that y = R sin t    and    x = R cos t

R ² = x ² + y ²    and    tan t = y / x

First we find R^2

R^2 = [4sqrt(3)]^2 + (-4)^2 = 48 + 16 = 64

R = 8

Now tan t = y/x = -4/4sqrt(3) = -1/sqrt(3) = -30 degrees

Hencethe polar co-ordinates are (R,t) = (8, -30^o)