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Sec

Sec[z]
gives the secant of z.
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • The argument of Sec is assumed to be in radians. (Multiply by Degree to convert from degrees.)
  • sec(z)=1/cos(z).
  • For certain special arguments, Sec automatically evaluates to exact values.
  • Sec can be evaluated to arbitrary numerical precision.
  • Sec automatically threads over lists.
EXAMPLESCLOSE ALL
Basic Examples   (5)
The argument is given in radians:
Use Degree to specify an argument in degrees:
Evaluate numerically:
The argument is given in radians:
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Use Degree to specify an argument in degrees:
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Evaluate numerically:
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Scope   (10)
Evaluate for complex arguments:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
The precision of the output can be much smaller or larger than the precision of the input:
Sec threads element-wise over lists and matrices:
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:
TraditionalForm formatting:
Generalizations & Extensions   (4)
Sec can deal with real-valued intervals:
Infinite arguments give symbolic results:
Apply Sec to a power series:
Sec threads over explicit lists as well as over sparse arrays:
Applications   (2)
Generate a plot with poles removed:
Generate a plot over the complex argument plane:
Properties & Relations   (11)
Basic parity and periodicity properties of the secant function get automatically applied:
Use TrigFactorList to factor Sec into Sin and Cos:
Complicated expressions containing trigonometric functions do not autosimplify:
Evaluate under additional assumptions:
Compositions with the inverse functions:
Solve a trigonometric equation:
Solve for zeros and poles:
Numerically solve a transcendental equation:
Integrals:
Sec is automatically returned as a special case for many mathematical functions:
Calculate residue symbolically and numerically:
Possible Issues   (5)
Machine-precision input is insufficient to give a correct answer:
With exact input, the answer is correct:
A larger setting for $MaxExtraPrecision is needed:
For arguments with imaginary part too large, the result cannot be represented by a computer:
Machine-number inputs can give high-precision results:
In traditional form parentheses are needed around the argument:
Neat Examples   (6)
Various integrals and products:
Plot Sec at integer points:
Generate the Sec function from integrals and sums:
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