Convert the rectangular point 3 3 squareroot 3 to polar coor

Convert the rectangular point (3, -3 squareroot 3) to polar coordinates.

Solution

The rectangular coordinates and polar coordinates are related as

R^2= x^2 + y^2        and    tan theta= y/x

Here x= 3 and y=-3sqrt3

therefore

R^2= 3^2 + (-3sqrt3)^2= 9 + 27=36

R^2=36

R=6

tan theta=-3sqrt3/3=-sqrt3

tan theta=-sqrt3

theta=tan^-1-sqrt3=-60 degree

Therefore the polar coordinate is (6,-60 degree)