重要公式

重要的三角函数公式

\[sin\alpha cos\beta=\frac{sin(\alpha+\beta)+sin(\alpha-\beta)}{2} \]

\[cos\alpha cos\beta=\frac{cos(\alpha+\beta)+cos(\alpha-\beta)}{2} \]

\[sin\alpha sin\beta=-\frac{cos(\alpha+\beta)-cos(\alpha-\beta)}{2} \]

\[cos(\alpha+\beta)=cos\alpha cos\beta-sin\alpha sin\beta \]

\[cos(\alpha-\beta)=cos\alpha cos\beta+sin\alpha sin\beta \]

\[sin(\alpha+\beta)=sin\alpha cos\beta+cos\alpha sin\beta \]

\[sin(\alpha-\beta)=sin\alpha cos\beta-cos\alpha sin\beta \]

\[sin2\alpha=2sin\alpha cos\alpha \]

\[cos2\alpha=cos^2\alpha-sin^2\alpha=2cos^2\alpha-1=1-2sin^2\alpha \]

\[tan2\alpha=\frac{2tan\alpha}{1-tan^2\alpha} \]

三角函数和复数

\[e^{i\theta}=cos\theta+isin\theta \]

\[e^{-i\theta}=cos\theta-isin\theta \]

\[cos\theta=\frac{e^{i\theta}+e^{-i\theta}}{2} \]

\[sin\theta=\frac{e^{i\theta-}e^{-i\theta}}{2i} \]