From Encyclopedia of Mathematics
Revision as of 17:12, 7 February 2011 by (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

The trigonometric function

another notation is: tg. Its domain of definition is the entire number axis with the exception of the points , . The tangent is an unbounded, odd and periodic (with as the smallest positive period) function. The tangent and the cotangent are connected by the relation

The inverse function to the tangent is called the arctangent.

The derivative of the tangent is:

The indefinite integral of the tangent is:

The tangent has a series expansion:

The tangent of a complex argument is a meromorphic function with zeros at the points , where .


The general term in the series expansion of the tangent is:

where are the Bernoulli numbers.

See also Trigonometric functions.

The addition formula of the tangent is:


[a1] M. Abramowitz, I.A. Stegun, "Handbook of mathematical functions" , Dover, reprint (1965) pp. 71ff
How to Cite This Entry:
Tangent. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by Yu.A. Gor'kov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article