Решете x=4sin(0.1t+0.5)

$$x = 4 \sin ( 0.1 t + 0.5 )$$

Реши за t (complex solution)

$$t=-10i\ln(\frac{i\sqrt{x^{2}-16}+ix}{4})+20\pi n_{1}-5\text{, }n_{1}\in \mathrm{Z}$$

$$t=-10i\ln(\frac{-i\sqrt{x^{2}-16}+ix}{4})+20\pi n_{2}-5\text{, }n_{2}\in \mathrm{Z}$$

Реши за x (complex solution)

$$x=2ie^{-\frac{it}{10}-0,5i}-2ie^{\frac{it}{10}+0,5i}$$

Реши за t

$$t=10\arcsin(\frac{x}{4})+20\pi n_{1}-5\text{, }n_{1}\in \mathrm{Z}$$

$$t=5\left(-2\arcsin(\frac{x}{4})+4\pi n_{2}+2\pi -1\right)\text{, }n_{2}\in \mathrm{Z}\text{, }|x|\leq 4$$

Реши за x

$$x=4\sin(\frac{t}{10}+0,5)$$