Risolvi y=10cos(2pit+pi/4)

$$y = 10 \cos ( 2 \pi t + \frac { \pi } { 4 } )$$

Trova t (soluzione complessa)

$$t=-\frac{i\ln(\frac{\sqrt{y^{2}-100}+y}{10})}{2\pi }+n_{1}-\frac{1}{8}\text{, }n_{1}\in \mathrm{Z}$$

$$t=-\frac{i\ln(\frac{-\sqrt{y^{2}-100}+y}{10})}{2\pi }+n_{2}-\frac{1}{8}\text{, }n_{2}\in \mathrm{Z}$$

Trova y (soluzione complessa)

$$y=5e^{-\frac{\pi \left(8it+i\right)}{4}}\left(e^{\frac{\pi \left(8it+i\right)}{2}}+1\right)$$

Trova t

$$t=\frac{\frac{4\arccos(\frac{y}{10})}{\pi }+8n_{1}-1}{8}\text{, }n_{1}\in \mathrm{Z}$$

$$t=\frac{-\frac{4\arccos(\frac{y}{10})}{\pi }+8n_{2}-1}{8}\text{, }n_{2}\in \mathrm{Z}\text{, }|y|\leq 10$$

Trova y

$$y=10\cos(\frac{\pi \left(8t+1\right)}{4})$$