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    Trigonometric Addition Formulas

    Alternate name

    angle addition formulas

    Basic definition

    The trigonometric addition formulas are a set of formulas that express trigonometric functions of sums of angles in terms of the trigonometric functions of the original angles.

    Detailed definition

    Angle addition formulas express trigonometric functions of sums of angles α ± β in terms of functions of α and β. The fundamental formulas of angle addition in trigonometry are given by sin(α + β) | = | sin α cos β + sin β cos α sin(α - β) | = | sin α cos β - sin β cos α cos(α + β) | = | cos α cos β - sin α sin β cos(α - β) | = | cos α cos β + sin α sin β tan(α + β) | = | (tan α + tan β)/(1 - tan α tan β) tan(α - β) | = | (tan α - tan β)/(1 + tan α tan β).

    Related terms

    double-angle formulas | half-angle formulas | harmonic addition theorem | multiple-angle formulas | prosthaphaeresis formulas | trigonometry | trigonometry angles | Werner formulas

    Educational grade level

    high school level (California trigonometry standard)

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