三角関数の公式

$$\begin{eqnarray*} \sin(x\pm y)&=& \sin x\cos y\pm\cos x\sin y \\ \cos(x\pm y)&=&\cos x\cos y\mp\sin x\sin y \end{eqnarray*}$$

$$\begin{eqnarray*} \cos x\cos y &=& \frac{1}{2}\left\{\cos(x-y)+\cos(x+y)\right\... ... \cos x\sin y &=& \frac{1}{2}\left\{\sin(x+y)-\sin(x-y)\right\} \end{eqnarray*}$$

$$\begin{eqnarray*} \cos^2 x&=& \frac{1}{2}\left\{1+\cos2x\right\}\\ \sin^2 x&=... ... \cos2x &=& \cos^2x-\sin^2x\\ &=&1-2\sin^2x\\ &=&2\cos^2x-1 \end{eqnarray*}$$

$$\cos^2x+\sin^2x=1$$

オイラーの式

$$e^{\pm jx}= \cos x\pm j\sin x$$

$$\begin{eqnarray*} \cos x&=&\frac{1}{2}\{e^{jx}+e^{-jx}\}\\ \sin x&=&\frac{1}{2j}\{e^{jx}-e^{-jx}\} \end{eqnarray*}$$