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ArcTan

ArcTan[z]
gives the arc tangent tan^(-1)(z) of the complex number z.
ArcTan[x, y]
gives the arc tangent of , taking into account which quadrant the point (x,y) is in.
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • All results are given in radians.
  • For real z, the results are always in the range -pi/2 to pi/2.
  • For certain special arguments, ArcTan automatically evaluates to exact values.
  • ArcTan can be evaluated to arbitrary numerical precision.
  • ArcTan automatically threads over lists.
  • ArcTan[z] has branch cut discontinuities in the complex z plane running from -i ∞ to -i and +i to +i ∞.
  • If x or y is complex, then ArcTan[x, y] gives . When x^2+y^2=1, ArcTan[x, y] gives the number phi such that x=cosphi and y=sinphi.
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