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Cot

Cot[z]
gives the cotangent of z.
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • The argument of Cot is assumed to be in radians. (Multiply by Degree to convert from degrees.)
  • cot(z)=1/tan(z).
  • For certain special arguments, Cot automatically evaluates to exact values.
  • Cot can be evaluated to arbitrary numerical precision.
  • Cot automatically threads over lists.
EXAMPLESCLOSE ALL
Basic Examples   (4)
The argument is given in radians:
Use Degree to specify an argument in degrees:
The argument is given in radians:
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Use Degree to specify an argument in degrees:
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Scope   (12)
Evaluate numerically:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
The precision of the output can be much smaller than the precision of the input:
Cot threads element-wise over lists and matrices:
Evaluate for complex arguments:
Simple exact values are generated automatically:
More complicated cases require explicit use of FunctionExpand:
Convert multiple-angle expressions:
Convert sums of trigonometric functions to products:
Expand assuming real variables:
Convert to complex exponentials:
TraditionalForm formatting:
Generalizations & Extensions   (4)
Cot can deal with real-valued intervals:
Infinite arguments give symbolic results:
Cot can be applied to power series:
Cot threads element-wise over sparse arrays as well as lists:
Applications   (3)
Generate a plot with poles removed:
Generate a plot over the complex argument plane:
The cotangent function conformally maps a parabola into the unit disk:
Properties & Relations   (12)
Basic parity and periodicity properties of the cotangent function are automatically applied:
Use TrigFactorList to factor Cot into Sin and Cos:
Complicated expressions containing trigonometric functions do not simplify automatically:
Simplify with assumptions on parameters:
Compose with inverse functions:
Solve a trigonometric equation:
Solve for zeros and poles:
Numerically find a root of a transcendental equation:
Integrals:
Cot appears in special cases of many mathematical functions:
Calculate residue symbolically and numerically:
Cot is a numeric function:
Possible Issues   (2)
Machine-precision input is insufficient to give a correct answer:
With exact input, the answer is correct:
A larger setting for $MaxExtraPrecision is needed:
Neat Examples   (6)
Plot Cot at integer points:
The continued fraction is highly regular:
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