Trigonometriai összefüggések | mateking
 

Trigonometriai összefüggések

\( \tan{x} = \frac{ \sin{x} }{ \cos{x} } \)

\( \cot{x} = \frac{ \cos{x} }{ \sin{x} } \)

\( \sin^2{\alpha} + \cos^2{\alpha} = 1 \quad \sin^2{\alpha} = 1-\cos^2{\alpha} \quad \cos^2{\alpha}=1-\sin^2{\alpha} \)

\( \cos{\alpha} = \sin{ \left( \frac{ \pi}{2} - \alpha \right) } \quad \cos{\alpha} = \sin{ \left( \alpha + \frac{ \pi}{2}\right) } \quad \sin{\alpha} = \sin{ ( \pi - \alpha) }\)

\( \sin{\alpha} = \cos{ \left( \frac{ \pi}{2} - \alpha \right) } \quad -\sin{\alpha} = \cos{ \left( \alpha + \frac{ \pi}{2}\right) } \quad -\cos{\alpha} = \cos{ ( \pi - \alpha) }\)

\( \sin{2\alpha} = 2 \sin{\alpha}\cos{\alpha} \quad \sin{(\alpha \pm \beta)} = \sin{\alpha} \cos{\beta} \pm \cos{\alpha} \sin{\beta} \)

\( \cos{2\alpha} = \cos^2{\alpha} - \sin^2{\alpha} \quad \cos{(\alpha \pm \beta )} = \cos{\alpha} \cos{\beta} \mp \sin{\alpha}\sin{\beta} \)

\( \sin^2{\alpha}=\frac{1-\cos{2 \alpha}}{2} \)

\( \cos^2{\alpha}=\frac{1+\cos{2 \alpha}}{2} \)