Convert the rectangular point 3 3 squareroot 3 to polar coor

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

Solution:

Remember that tangent = y/x. So tan() = y/x and arctan(y/x) =

Also, r^2 = x^2 + y^2. So we have:

Polar Form = (r, ) = (sqrt(x^2 + y^2), tan^-1(y/x))

At point (3, -3sqrt(3));

r^2 = (3)^2 + (-3sqrt(3))^2 = 9 + 27 = 36 = +/- 6

= arctan(y/x) = arctan(-3sqrt(3) / 3) = arctan(-sqrt(3)) = -/3

so polar coordinates (r, ) = (6, -/3)