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

Sine of a double angle

sin⁡2α=2sin⁡αcos⁡α\sin 2\alpha=2\sin\alpha\cos\alpha

Result unit: — (liczba)

What it describes

The sine of a double angle expressed through the sine and cosine of the angle.

Symbols

α\alpha
angle

Where it comes from

The sine of a double angle is expressed through the sine and cosine of the single angle — useful in equations and integrals.

When to use it

Trigonometric equations, simplification, integrals.

Example

sin⁡α=0.6\sin\alpha=0.6, cos⁡α=0.8\cos\alpha=0.8. Find sin⁡2α\sin2\alpha.
Substitution2⋅0.6⋅0.82\cdot0.6\cdot0.8.
Resultsin⁡2α=0.96\sin2\alpha=0.96.

Related formulas

Cosine of a double angle Sine of a sum or difference of angles

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