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ArcCot

ArcCot[z]
gives the arc cotangent cot^(-1)(z) of the complex number z.
  • 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, excluding 0.
  • For certain special arguments, ArcCot automatically evaluates to exact values.
  • ArcCot can be evaluated to arbitrary numerical precision.
  • ArcCot automatically threads over lists.
  • ArcCot[z] has a branch cut discontinuity in the complex z plane running from -i to +i.
EXAMPLESCLOSE ALL
Scope   (7)
Evaluate numerically:
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 transformation is automatically applied:
ArcCot threads element-wise over lists:
TraditionalForm formatting:
Generalizations & Extensions   (3)
Infinite arguments give symbolic results:
ArcCot can be applied to a power series:
ArcCot can deal with real-valued intervals:
Applications   (4)
Find angles of the right triangle with sides 3, 4 and hypotenuse 5:
They total to 90°:
Addition theorem for cotangent function:
Solve a differential equation:
Branch cut of ArcCot runs along the imaginary axis:
Properties & Relations   (3)
Use TrigToExp to express ArcCot using Log:
Use FullSimplify to simplify expressions with ArcCot:
Use Reduce to solve inequalities involving ArcCot:
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