Question

Convert rectangular coordinates (4,-4) into polar coordinates, in the interval (-pi, pi)

Answer 1

well, theta = atan(y/x) = atan(-1)
Now, there are two angles with tangent of -1, namely -pi/4 and 3pi/4; consideration of the quadrant we are in (quadrant II) shows that the angle is 3pi/4
then the radius is r = sqrt(4^2 + (-4)^2) = sqrt(32) = 4sqrt(2)

Answer 2

\(r=\sqrt{x^2+y^2}\)

\(\theta =\tan^{-1}\dfrac{y}{x}\)