Vyřešit x=5sin((1+pi/4)t)

$$x = 5 \sin ( (1+ \frac{ \pi }{ 4 } ) t)$$

Vyřešte pro: t (complex solution)

$$t=\frac{4i\ln(\frac{i\left(\sqrt{x^{2}-25}+x\right)}{5})}{-\pi -4}-\frac{8\pi n_{1}}{-\pi -4}\text{, }n_{1}\in \mathrm{Z}$$

$$t=\frac{4i\ln(\frac{-i\sqrt{x^{2}-25}+ix}{5})}{-\pi -4}-\frac{8\pi n_{2}}{-\pi -4}\text{, }n_{2}\in \mathrm{Z}$$

Vyřešte pro: t

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

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

Vyřešte pro: x

$$x=5\sin(\frac{\left(\pi +4\right)t}{4})$$