Consider a point with rectangular coordinates (x, y). If x<0 then the polar coordinates of the point are (r,θ) where r≥0 and −π/2≤θ<3π/2and:

r=

θ=

If x≥0 then the polar coordinates of the point are (r,θ) where r≥0 and −π/2≤θ<3π/2 and:

r=

θ=​

Step-by-step explanation:

I see a major problem with this question in that the possible range for θ is VERY narrow...mostly because -π/2 = 3π/2

That would lead to θ = -π/2 and force x = 0 and y = r and make the whole situation a rather moot question.

IF we ASSUME that it is supposed to be  π/2 ≤ θ ≤ 3π/2

THEN I would suggest that θ = π + arctan(y/x) radians

We need to add π to get the result into the second or third quadrants

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stops on an even number.