“Tangent”的概念、定义、习题解题方法及翻译-数学辞典

单词

Tangent

释义

Tangent

The tangent function is defined by

(1)

where

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)

Lambert derived another Continued Fraction expression for the tangent,

(4)

An interesting identity involving the Product of tangents is

(5)

where

is the Floor Function. Another tangent identity is

(6)

(Beeler et al. 1972, Item 16).

See also Alternating Permutation, Cosine, Cotangent, Inverse Tangent, Morrie's Law,Sine, Tangent Line, Tangent Plane

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.

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