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    Half-angle Identities

    Alternate names

    half-angle identities | trigonometric half-angle identities

    Basic definition

    A set of formulas that express trigonometric functions of half an angle in terms of the trigonometric functions of the original angle.

    Detailed definition

    Half-angle formulas and formulas expressing trigonometric functions of an angle x/2 in terms of functions of an angle x. For real x, sin(1/2 x) | = | (-1)^(⌊x/(2π)⌋) sqrt((1 - cos x)/2) cos(1/2 x) | = | (-1)^(⌊(x + π)/(2π)⌋) sqrt((1 + cos x)/2) tan(1/2 x) | = | (-1)^(⌊x/π⌋) sqrt((1 - cos x)/(1 + cos x)) | = | (sin x)/(1 + cos x) | = | (1 - cos x)/(sin x) | = | (tan x sin x)/(tan x + sin x) | = | ((-1)^(⌊(x + π/2)/π⌋) sqrt(1 + tan^2 x) - 1)/(tan x).

    Related terms

    double-angle formulas | hyperbolic functions | multiple-angle formulas | prosthaphaeresis formulas | trigonometric addition formulas | trigonometric functions | trigonometry | Weierstrass substitution

    Educational grade level

    high school level (California trigonometry standard)

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