y=-2sin(2x+pi/4) を解きます| Microsoft 数学ソルバー

$$y = - 2 \sin ( 2 x + \frac { \pi } { 4 } )$$

x を解く (複素数の解)

$$x=-\frac{i\ln(\frac{i\sqrt{y^{2}-4}-iy}{2})}{2}+\pi n_{1}-\frac{\pi }{8}\text{, }n_{1}\in \mathrm{Z}$$

$$x=-\frac{i\ln(\frac{-i\sqrt{y^{2}-4}-iy}{2})}{2}+\pi n_{2}-\frac{\pi }{8}\text{, }n_{2}\in \mathrm{Z}$$

y を解く (複素数の解)

$$y=ie^{2ix+\frac{\pi i}{4}}-ie^{-2ix-\frac{\pi i}{4}}$$

x を解く

$$x=\frac{-4\arcsin(\frac{y}{2})+8\pi n_{1}-\pi }{8}\text{, }n_{1}\in \mathrm{Z}$$

$$x=\frac{4\arcsin(\frac{y}{2})+8\pi n_{2}+3\pi }{8}\text{, }n_{2}\in \mathrm{Z}\text{, }|y|\leq 2$$

y を解く

$$y=-2\sin(\frac{8x+\pi }{4})$$