Giải S=3sin(2t+5)

$$S = 3 \sin ( 2 t + 5 )$$

Tìm S (complex solution)

$$S=\frac{3ie^{-2it-5i}-3ie^{2it+5i}}{2}$$

Tìm t (complex solution)

$$t=-\frac{i\ln(\frac{i\sqrt{S^{2}-9}+iS}{3})}{2}+\pi n_{1}-\frac{5}{2}\text{, }n_{1}\in \mathrm{Z}$$

$$t=-\frac{i\ln(\frac{-i\sqrt{S^{2}-9}+iS}{3})}{2}+\pi n_{2}-\frac{5}{2}\text{, }n_{2}\in \mathrm{Z}$$

Tìm S

$$S=3\sin(2t+5)$$

Tìm t

$$t=\frac{\arcsin(\frac{S}{3})+2\pi n_{1}-5}{2}\text{, }n_{1}\in \mathrm{Z}$$

$$t=\frac{-\arcsin(\frac{S}{3})+2\pi n_{2}+\pi -5}{2}\text{, }n_{2}\in \mathrm{Z}\text{, }|S|\leq 3$$