三角函数公式整理

诱导公式

奇变偶不变，符号看象限
\[ \begin{aligned} &\cos {\left(\pi + \alpha \right)} =-\cos \alpha\\ &\sin {\left( \pi + \alpha \right) } = -\sin \alpha\\ &\tan {\left( \pi + \alpha \right)} = \tan \alpha \end{aligned} \]

\[ \begin{aligned} &\cos {\left(-\alpha \right)} =\cos \alpha\\ &\sin {\left(-\alpha \right) } = -\sin \alpha\\ &\tan {\left(-\alpha \right)} = -\tan \alpha \end{aligned} \]

\[ \begin{aligned} &\cos {\left(\pi - \alpha \right)} =-\cos \alpha\\ &\sin {\left( \pi - \alpha \right) } = \sin \alpha\\ &\tan {\left( \pi - \alpha \right)} = -\tan \alpha \end{aligned} \]

\[ \begin{aligned} &\cos {\left(\frac \pi 2 - \alpha \right)} =\sin \alpha\\ &\sin {\left( \frac \pi 2 - \alpha \right) } = \cos \alpha\\ \end{aligned} \]

\[ \begin{aligned} &\cos {\left(\frac \pi 2 + \alpha \right)} =-\sin \alpha\\ &\sin {\left( \frac \pi 2 + \alpha \right) } = \cos \alpha\\ \end{aligned} \]