This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

ArcTan

 ArcTan[z]gives the arc tangent of the complex number . ArcTangives the arc tangent of , taking into account which quadrant the point is in.
• Mathematical function, suitable for both symbolic and numerical manipulation.
• All results are given in radians.
• For real , the results are always in the range to .
• 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 plane running from to and to .
• If or is complex, then ArcTan gives . When , ArcTan gives the number such that and .
Divide by Degree to get results in degrees:
ArcTan gives the angle of the point :
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Divide by Degree to get results in degrees:
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ArcTan gives the angle of the point :
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 Out[2]=

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 Scope   (6)
Evaluate for complex arguments:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Simple exact values are generated automatically:
Parity transformations are automatically applied:
Infinite arguments give symbolic results:
ArcTan can be applied to a power series:
ArcTan can deal with real-valued intervals:
 Applications   (5)
Find angles of the right triangle with sides 3, 4 and hypotenuse 5:
They total to 90°:
Find integrals of rational functions in terms of ArcTan: