Formulas & tables/Mathematics/Trigonometry/Cosine of a double angle

Cosine of a double angle

cos⁡2α=cos⁡2α−sin⁡2α\cos 2\alpha=\cos^2\alpha-\sin^2\alpha

Result unit: — (liczba)

What it describes

The cosine of a double angle expressed through the functions of the angle.

Symbols

α\alpha
angle

Where it comes from

The cosine of a double angle; using the Pythagorean identity it also has the forms 1−2sin⁡2α1-2\sin^2\alpha and 2cos⁡2α−12\cos^2\alpha-1.

When to use it

Trigonometric equations and identities, integrals.

Example

sin⁡α=0.6\sin\alpha=0.6, cos⁡α=0.8\cos\alpha=0.8. Find cos⁡2α\cos2\alpha.
Substitution0.82−0.620.8^2-0.6^2.
Resultcos⁡2α=0.64−0.36=0.28\cos2\alpha=0.64-0.36=0.28.

Related formulas

Sine of a double angle Pythagorean trigonometric identity

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