The tangent function is defined by

(1) |

The Maclaurin Series for the tangent function is

(2) |

where is a Bernoulli Number.

is Irrational for any Rational , which can be
proved by writing as a Continued Fraction

(3) |

(4) |

An interesting identity involving the Product of tangents is

(5) |

(6) |

**References**

Abramowitz, M. and Stegun, C. A. (Eds.). ``Circular Functions.'' §4.3 in
*Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.*
New York: Dover, pp. 71-79, 1972.

Beeler, M.; Gosper, R. W.; and Schroeppel, R. *HAKMEM.* Cambridge, MA: MIT Artificial Intelligence Laboratory, Memo AIM-239, Feb. 1972.

Spanier, J. and Oldham, K. B. ``The Tangent and Cotangent Functions.''
Ch. 34 in *An Atlas of Functions.* Washington, DC: Hemisphere, pp. 319-330, 1987.

© 1996-9

1999-05-26