Mathematica has functions ArcCos, ArcSin, and ArcTan, but none of these does what I need, which is, given two real numbers a and b, at least one of them being nonzero, to find the angle x such that

{Cos[x], Sin[x]} == {a,b}/Sqrt[a^2+b^2].

Is there a simple way to build such a function? Thanks for any help.

  • 1
    $\begingroup$ There's a reason why I'm not called bobthemathematician, but how about rolling your own? Solve[{Cos[x] == a/Sqrt[a^2 + b^2], Sin[x] == b/Sqrt[a^2 + b^2]}, x] $\endgroup$ Nov 12, 2014 at 4:00
  • 8
    $\begingroup$ ArcTan[a, b] does what you want. $\endgroup$
    – user484
    Nov 12, 2014 at 4:10
  • $\begingroup$ ArcTan[a,b] is the best answer in terms of efficiency but was entered as a comment so it could not be accepted. The answer by HaoLiang and Kuba also works and provides good insight. $\endgroup$
    – Soldalma
    Nov 12, 2014 at 12:53

1 Answer 1


You can use this

Arg[#1 + I*#2] &[a, b]
  • $\begingroup$ How is this different from ArcTan[#1,#2]&[a,b]? $\endgroup$
    – Ruslan
    Feb 14, 2016 at 7:53

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