Atan2

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"Oh, right, tan ^{− 1} sometimes gets the quadrant wrong. What a gyp." --Dani Fong, frequently

[edit] Outline

atan2, a function of C and other sensible languages (but not mainstream mathematics?!?) is a sensible version of the arctangent tan ^{− 1} which doesn't mess up the quadrant at inopportune times. It is defined as φ in the solution to

atan2(y,x) = φ, such that e^iφ = x + iy