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Triple-Angle Formulas

The triple-angle formulas express trigonometric functions of three times an angle in terms of trigonometric functions of the angle:

sin(3x)=3sinx-4sin^3x
(1)
cos(3x)=4cos^3x-3cosx
(2)
tan(3x)=(3tanx-tan^3x)/(1-3tan^2x),
(3)

where the tangent identity is understood where both sides are defined. They follow by applying the trigonometric addition formulas twice.

See also

Double-Angle Formulas, Half-Angle Formulas, Multiple-Angle Formulas, Trigonometric Addition Formulas

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References

Harris, J. W. and Stocker, H. Handbook of Mathematics and Computational Science. New York: Springer-Verlag, 1998.

Cite this as:

Weisstein, Eric W. "Triple-Angle Formulas." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Triple-AngleFormulas.html

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