[Rd] Add to Documentation of atan2.

[Jorgen Harmse]

The current documentation says that atan2(y,x) is the angle between the x-axis and the vector from the origin to (x,y), but what does this mean when x & y are complex? The function seems to pick theta with Re(theta) between -pi and pi and with tan(theta) (approximately) equal to y/x, but that leaves 2 (sometimes 3) options, and there must be a set (branch region with 3 real dimensions?) on which the function is discontinuous. Please add details.

Even for real inputs, it might help to spell out the behaviour on the negative x-axis. It mostly matches the branch-cut rules for the other functions, but atan2(0,0)==0 is a unexpected.

I also suggest ‘See Also’ links from trigonometric functions to hyperbolic functions and from hyperbolic functions to exponential & logarithmic functions.

Regards,
Jorgen Harmse.



> R.version.string

[1] "R version 4.0.4 (2021-02-15)"






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