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 \[ \cos^5\alpha = \frac{10 \cos\alpha + 5 \cos 3\alpha + \cos 5\alpha}{16} \]