Tangent
The tangent function is defined by
 | (1) |
is the Sine function and 
is the Cosine function. The word ``tangent,'' however, alsohas an important related meaning as a Line or Plane which touches a given curve or solid at a single point. These geometrical objects are then called a Tangent Line or Tangent Plane, respectively.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) |
is the Floor Function. Another tangent identity is | (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.
- Umbilic Point
- Umbral Calculus
- Umbrella
- Unambiguous
- Unbiased
- Uncia
- Uncorrelated
- Uncountable Set
- Uncountably Infinite Set
- Undecagon
- Undecidable
- Undecillion
- Undetermined Coefficients Method
- Undulating Number
- Unduloid
- Unexpected Hanging Paradox
- Unfinished Game
- Unhappy Number
- Unicursal Circuit
- Uniform Apodization Function
- Uniform Boundedness Principle
- Uniform Convergence
- Uniform Distribution
- Uniform Polyhedron
- Uniform Variate