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

# Tan

 Tan[z]gives the tangent of .
• Mathematical function, suitable for both symbolic and numerical manipulation.
• The argument of Tan is assumed to be in radians. (Multiply by Degree to convert from degrees.)
• Tan is automatically evaluated when its argument is a simple rational multiple of ; for more complicated rational multiples, FunctionExpand can sometimes be used.
• For certain special arguments, Tan automatically evaluates to exact values.
• Tan can be evaluated to arbitrary numerical precision.
• Tan automatically threads over lists.
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   (11)
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:
Tan threads element-wise over lists and matrices:
Tan can take complex number inputs:
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:
Tan can deal with real-valued intervals:
Infinite arguments give symbolic results:
Tan can be applied to power series:
Tan threads element-wise over sparse arrays as well as lists:
 Applications   (5)
Generate a plot with poles removed:
Generate a plot over the complex argument plane:
Differential equation solution with a movable singularity:
The tangent function conformally maps a parabola into the unit disk:
Pursuit curve in the reference frame of the predator with prey moving half as fast along a line:
Basic parity and periodicity properties of the tangent function get automatically applied:
Use TrigFactorList to factor Tan into Sin and Cos:
Complicated expressions containing trigonometric functions do not simplify automatically:
Simplify under 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:
Tan appears in special cases of many mathematical functions:
Calculate residue symbolically and numerically:
Tan is a numeric function:
Machine-precision input is insufficient to give a correct answer:
With exact input, the answer is correct:
A larger setting for \$MaxExtraPrecision is needed:
In traditional form parentheses are needed around the argument:
Plot Tan at integer points:
The continued fraction is highly regular: