Tan

Tan[z]
gives the tangent of .

DetailsDetails

  • 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.)
  • Sin[z]/Cos[z] is automatically converted to Tan[z]. TrigFactorList[expr] does decomposition.
  • 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.

Background
Background

  • Tan is the tangent function, which is one of the basic functions encountered in trigonometry. Tan[x] is defined as the ratio of the corresponding sine and cosine functions: . The equivalent schoolbook definition of the tangent of an angle in a right triangle is the ratio of the length of the leg opposite to the length of the leg adjacent to it.
  • Tan threads element-wise over lists and matrices. When given numbers as arguments, Tan may be evaluated to arbitrary numeric precision. MatrixFunction can be used to give the tangent of a square matrix (i.e. the power series for the tangent function with ordinary powers replaced by matrix powers) as opposed to the tangent of the individual matrix elements.
  • Tan automatically evaluates to exact values when its argument is a simple rational multiple of . For more complicated rational multiples, FunctionExpand can sometimes be used to obtain an explicit exact value. TrigFactorList can be used to factor expressions involving Tan into terms containing Sin and Cos. Other operations useful for manipulation of symbolic expressions involving Tan include TrigToExp, TrigExpand, Simplify, and FullSimplify.
  • Tan satisfies the identity , which is equivalent to the Pythagorean theorem. The definition of the tangent function is extended to complex arguments using the definition , where is the base of the natural logarithm. Tan has poles at values for an integer where it evaluates to ComplexInfinity.
  • The inverse function of Tan is ArcTan. The hyperbolic tangent is given by Tanh.
Introduced in 1988
(1.0)
| Updated in 1999
(4.0)