حل x=5sin(pi/6t+2/3pi)

$$x = 5 \sin ( \frac { \pi } { 6 } t + \frac { 2 } { 3 } \pi )$$

حل مسائل t (complex solution)

$$t=-\frac{6i\ln(\frac{i\sqrt{x^{2}-25}+ix}{5})}{\pi }+12n_{1}-4\text{, }n_{1}\in \mathrm{Z}$$

$$t=-\frac{6i\ln(\frac{-i\sqrt{x^{2}-25}+ix}{5})}{\pi }+12n_{2}-4\text{, }n_{2}\in \mathrm{Z}$$

حل مسائل t

$$t=2\left(\frac{3\arcsin(\frac{x}{5})}{\pi }+6n_{1}-2\right)\text{, }n_{1}\in \mathrm{Z}$$

$$t=2\left(-\frac{3\arcsin(\frac{x}{5})}{\pi }+6n_{2}+1\right)\text{, }n_{2}\in \mathrm{Z}\text{, }|x|\leq 5$$

حل مسائل x

$$x=5\sin(\frac{\pi \left(t+4\right)}{6})$$