カテゴリー: 三角関数

\[ \tan\frac{z}{2}=\frac{\sin z}{1+\cos z} \]

\[ \sin z=\frac{2\tan\frac{z}{2}}{1+\tan^{2}\frac{z}{2}} \]

\[ \int\frac{1}{\alpha\sin z+\beta\cos z+\gamma}dz=-\frac{2}{\sqrt{\alpha^{2}+\beta^{2}-\gamma^{2}}}\tanh^{\bullet}\frac{\left(\gamma-\beta\right)\tan\frac{z}{2}+\alpha}{\sqrt{\alpha^{2}+\beta^{2}-\gamma^{2}}}+C \]

\[ \sin^{\bullet}\sin z=?z \]

\[ \sin\Arg z=\frac{\Im z}{\left|z\right|} \]

\[ \cos z\pm i\sin z=e^{\pm iz} \]

\[ 1\pm i\tan z=\frac{1}{\cos\left(2\Re z\right)+\cosh\left(2\Im z\right)}\left(e^{\pm2i\Re z}+e^{\mp2\Im z}\right) \]

\[ \sin z=\sin\left(\Re z\right)\cosh\left(\Im z\right)+i\cos\left(\Re z\right)\sinh\left(\Im z\right) \]

\[ \Sin^{\bullet}\left(iz\right)=i\Sinh^{\bullet}z \]

\[ \Sin^{\bullet}\left(-z\right)=-\Sin^{\bullet}z \]