Research website of Vyacheslav Gorchilin
All formulas
Formula. Math. Trigonometry
The product of the degree functions
$\sin \alpha \cdot \sin \beta$
$\sin \alpha \cdot \cos \beta$
$\cos \alpha \cdot \cos \beta$
$\sin^2\alpha \cdot \cos^2\alpha$
$\sin^3\alpha \cdot \cos^3\alpha$
$\sin^4\alpha \cdot \cos^4\alpha$
$\sin^5\alpha \cdot \cos^5\alpha$
$\sin^2\alpha$
$\sin^3\alpha$
$\sin^4\alpha$
$\sin^5\alpha$
$\cos^2\alpha$
$\cos^3\alpha$
$\cos^4\alpha$
$\cos^5\alpha$
The product of sines $\sin \alpha \cdot \sin \beta = \frac{\cos (\alpha - \beta) - \cos (\alpha + \beta)}{2}$
The product of the sine and cosine of $\sin \alpha \cdot \cos \beta = \frac{\sin (\alpha + \beta) + \sin (\alpha - \beta)}{2}$
The product of the cosines $\cos \alpha \cdot \cos \beta = \frac{\cos (\alpha - \beta) + \cos (\alpha + \beta)}{2}$
The product of the squares of the sine and cosine of $\sin^2\alpha \cdot \cos^2\alpha = \frac{1 - \cos 4\alpha}{8}$
The product of the cube of the sine and cosine of $\sin^3\alpha \cdot \cos^3\alpha = \frac{3\sin 2\alpha - \sin 6\alpha}{32}$
The product of sine and cosine to the fourth power $\sin^4\alpha \cdot \cos^4\alpha = \frac{3-4\cos 4\alpha + \cos 8\alpha}{128}$
The product of sine and cosine to the fifth power $\sin^5\alpha \cdot \cos^5\alpha = \frac{10\sin 2\alpha - 5\sin 6\alpha + \sin 10\alpha}{512}$
The square of the sine $\sin^2\alpha = \frac{1 - \cos 2\alpha}{2}$
Cube of the sine $\sin^3\alpha = \frac{3 \sin\alpha - \sin 3\alpha}{4}$
Fourth degree sine $\sin^4\alpha = \frac{3 - 4 \cos 2\alpha + \cos 4\alpha}{8}$
The fifth degree of the sine $\sin^5\alpha = \frac{10 \sin\alpha - 5 \sin 3\alpha + \sin 5\alpha}{16}$
The square of the cosine of $\cos^2\alpha = \frac{1 + \cos 2\alpha}{2}$
The cube of the cosine of $\cos^3\alpha = \frac{3 \cos\alpha + \cos 3\alpha}{4}$
The fourth power of the cosine of $\cos^4\alpha = \frac{3 + 4 \cos 2\alpha + \cos 4\alpha}{8}$
The fifth degree of the cosine of $\cos^5\alpha = \frac{10 \cos\alpha + 5 \cos 3\alpha + \cos 5\alpha}{16}$