Cartesian to Polar: Angle Theta Interval Defined

[jamesb1]

When it comes to converting Cartesian to polar coordinates, I sometimes still get mixed up on how to define the angle theta (if its -π <= theta <= π , or 0 <= theta <= 2π for example) depending on the position of the surface etc. Can anyone shed light on the definitive way on how to set this interval depending on different circumstances?

Thank you in advance for any help given!

 

[Simon Bridge]

Generally the polar angle is measured anticlockwise (viewed down the z-axis) from the +x axis, so your two examples are equivalent. eg $3\pi/2 = -\pi/2$
So you can set it up whichever way makes the math easier.