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=
For both r is r=sqrt(x^2+y^2) I'm sure what the angle would be.

4 answers

I'm not sure about the angle
Your answers should be expressions in terms of x and y)
x<0 means QII,QIII so π/2≤θ<3π/2
x>0 means QI, QIV, so -π/2≤θ<π/2
In any case, tanθ = y/x unless x=0
The second ones theta is tan(theta) =y/x
But the first one is different