Giải a=2sin(θ+frac{sqrt{2}}{2})

$$a = 2 \sin ( \theta + \frac { \sqrt { 2 } } { 2 } )$$

Tìm a (complex solution)

$$a=ie^{-i\theta -\frac{\sqrt{2}i}{2}}-ie^{i\theta +\frac{\sqrt{2}i}{2}}$$

Tìm θ (complex solution)

$$\theta =-i\ln(\frac{i\sqrt{a^{2}-4}+ia}{2})+2\pi n_{1}-\frac{\sqrt{2}}{2}\text{, }n_{1}\in \mathrm{Z}$$

$$\theta =-i\ln(\frac{-i\sqrt{a^{2}-4}+ia}{2})+2\pi n_{2}-\frac{\sqrt{2}}{2}\text{, }n_{2}\in \mathrm{Z}$$

Tìm a

$$a=2\sin(\frac{\sqrt{2}\left(\sqrt{2}\theta +1\right)}{2})$$

Tìm θ

$$\theta =\frac{2\arcsin(\frac{a}{2})+4\pi n_{1}-\sqrt{2}}{2}\text{, }n_{1}\in \mathrm{Z}$$

$$\theta =\frac{-2\arcsin(\frac{a}{2})+4\pi n_{2}+2\pi -\sqrt{2}}{2}\text{, }n_{2}\in \mathrm{Z}\text{, }|a|\leq 2$$