求解 y=2sin(pi/3-x)

$$y=2 \sin ( \frac{ \pi }{ 3 } -x )$$

求解 x 的值 (复数求解)

$$x=\frac{3i\ln(\frac{i\left(\sqrt{y^{2}-4}+y\right)}{2})+\pi }{3}+2\pi n_{1}\text{, }n_{1}\in \mathrm{Z}$$

$$x=\frac{3i\ln(\frac{-i\sqrt{y^{2}-4}+iy}{2})+\pi }{3}+2\pi n_{2}\text{, }n_{2}\in \mathrm{Z}$$

求解 y 的值 (复数求解)

$$y=ie^{ix-\frac{\pi i}{3}}-ie^{-ix+\frac{\pi i}{3}}$$

求解 x 的值

$$x=\frac{-3\arcsin(\frac{y}{2})+6\pi n_{1}+\pi }{3}\text{, }n_{1}\in \mathrm{Z}$$

$$x=\frac{3\arcsin(\frac{y}{2})+6\pi n_{2}-2\pi }{3}\text{, }n_{2}\in \mathrm{Z}\text{, }|y|\leq 2$$

求解 y 的值

$$y=2\sin(\frac{\pi -3x}{3})$$