This question has a list of equations used when converting between rectangular and polar coordinates.
In this case, we will be using
{(r^2 = x^2 + y^2), (tan(theta)=y/x):}
=>{(r = sqrt(x^2 + y^2)), (theta = tan^(-1)(y/x)):}
r = sqrt((-23)^2 + (-3)^2)
theta = tan^(-1)((-3)/(-23)))^(color(red)("*"))
" "^color(red)("*")(While calculating theta, the -3 and -23 cancel negatives, causing the resulting angle puts us in quadrant I when we want quadrant III. To fix this, all we need to do is add or subtract pi from the angle to put us in the correct quadrant.)
=>{(r = sqrt(538)), (theta = tan^(-1)(3/23)+pi):}
Thus we get the polar form of (-23, -3) to be
(sqrt(538), tan^(-1)(3/23)+pi) ~~ (23.195, 3.271)
