13.2: Identidades trigonométricas

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El seno y el coseno son periódicos, lo que lleva a las siguientes identidades:

\[\sin\theta =-\sin\left ( -\theta \right )=-\cos(\theta +\frac{\pi }{2})=\cos(\theta -\frac{\pi }{2})\]

\[\cos\theta =\cos\left ( -\theta \right )=\sin(\theta +\frac{\pi }{2})=-\sin(\theta -\frac{\pi }{2})\]

El seno o coseno para sumas o diferencias entre ángulos se puede calcular utilizando las siguientes identidades:

\[\cos(\theta _{1}+\theta _{2})=\cos(\theta _{1})\cos(\theta _{2})-\sin(\theta _{1})\sin(\theta _{2})\]

\[\sin(\theta _{1}+\theta _{2})=\sin(\theta _{1})\cos(\theta _{2})+\cos(\theta _{1})\sin(\theta _{2})\]

\[\cos(\theta _{1}-\theta _{2})=\cos(\theta _{1})\cos(\theta _{2})+\sin(\theta _{1})\sin(\theta _{2})\]

\[\sin(\theta _{1}-\theta _{2})=\sin(\theta _{1})\cos(\theta _{2})-\cos(\theta _{1})\sin(\theta _{2})\]

La suma de los cuadrados de seno y coseno para el mismo ángulo es uno:

\[\cos(\theta )\cos(\theta )+\sin(\theta )\sin(\theta )=1\]