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ArcTan

ArcTan[z]
gives the arc tangent of the complex number .
ArcTan
gives the arc tangent of , taking into account which quadrant the point is in.
MORE INFORMATION
  • 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 .
EXAMPLESCLOSE ALL
Basic Examples   (5)
Results are in radians:
Divide by Degree to get results in degrees:
ArcTan gives the angle of the point :
Results are in radians:
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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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Scope   (6)
Evaluate for complex arguments:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
ArcTan threads element-wise over lists:
Simple exact values are generated automatically:
Parity transformations are automatically applied:
TraditionalForm formatting:
Generalizations & Extensions   (3)
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:
Addition theorem for tangent function:
Solve a differential equation:
Branch cuts of ArcTan run along the imaginary axis:
Properties & Relations   (4)
Use TrigToExp to express ArcTan using Log:
Use FullSimplify to simplify expressions with ArcTan:
ArcTan is a special case of some special functions:
Use Reduce to solve inequalities involving ArcTan:
Possible Issues   (1)
Because ArcTan is a multivalued function,
This differs from the original argument by a factor of :
Neat Examples   (1)
Expansion about the branch point :
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