Fórmulas de trigonometría

Relaciones entre razones trigonométricas.

$\mbox{tg}\,\alpha=\dfrac{\mbox{sen}\,\alpha}{\cos\alpha}\\\\\mbox{sen}\,\alpha=\cos(\alpha-\frac{\pi}2)\\\\\text{sec}\,\alpha=\dfrac1{\cos\alpha}\\\\\text{cosec}\,\alpha=\dfrac1{\text{sen}\,\alpha}\\\\\text{cotg}\,\alpha=\dfrac1{\text{tg}\,\alpha}$

Fórmulas fundamentales de la trigonometría.

$\cos^2\alpha+\mbox{sen}^2\alpha=1\\\\1+\mbox{tg}^2\alpha=\sec^2\alpha\\\\\mbox{cotg}^2\alpha+1=\mbox{cosec}^2\alpha$

Fórmulas de la suma y resta de ángulos.

$\mbox{sen}(\alpha+\beta)=\mbox{sen}\alpha\cos\beta+\mbox{sen}\beta\cos\alpha\\\mbox{sen}(\alpha-\beta)=\mbox{sen}\alpha\cos\beta-\mbox{sen}\beta\cos\alpha\\\\\cos(\alpha+\beta)=\cos\alpha\cos\beta-\mbox{sen}\alpha\,\mbox{sen}\beta\\\cos(\alpha-\beta)=\cos\alpha\cos\beta+\mbox{sen}\alpha\,\mbox{sen}\beta\\\\\mbox{tg}(\alpha+\beta)=\dfrac{\mbox{tg}\alpha+\mbox{tg}\beta}{1-\mbox{tg}\alpha\,\mbox{tg}\beta}\\\\\mbox{tg}(\alpha-\beta)=\dfrac{\mbox{tg}\alpha-\mbox{tg}\beta}{1+\mbox{tg}\alpha\,\mbox{tg}\beta}$

Fórmulas del ángulo doble.

$\mbox{sen}(2\alpha)=2\,\mbox{sen}\alpha\cos\alpha\\\\\cos(2\alpha)=\cos^2\alpha-\mbox{sen}^2\alpha\\\\\mbox{tg}(2\alpha)=\dfrac{2\mbox{tg}\alpha}{1-\mbox{tg}^2\alpha}$

Fórmulas del ángulo mitad.

$\mbox{sen}(\frac{\alpha}2)=\pm\sqrt{\dfrac{1-\cos\alpha}2}\\\\\cos(\frac{\alpha}2)=\pm\sqrt{\dfrac{1+\cos\alpha}2}\\\\\mbox{tg}(\frac{\alpha}2)=\pm\sqrt{\dfrac{1-\cos\alpha}{1+\cos\alpha}}$

Fórmulas de transformación de sumas y restas en productos.

$\mbox{sen}\alpha+\mbox{sen}\beta=2\,\mbox{sen}(\frac{\alpha+\beta}2)\cos(\frac{\alpha-\beta}2)\\\mbox{sen}\alpha-\mbox{sen}\beta=2\,\mbox{sen}(\frac{\alpha-\beta}2)\cos(\frac{\alpha+\beta}2)\\\\\cos\alpha+\cos\beta=2\cos(\frac{\alpha+\beta}2)\cos(\frac{\alpha-\beta}2)\\\cos\alpha-\cos\beta=-2\,\mbox{sen}(\frac{\alpha+\beta}2)\,\mbox{sen}(\frac{\alpha-\beta}2)$

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