Risolvi r=3sin3varphi

$$r = 3 \sin 3 \varphi$$

Trova φ (soluzione complessa)

$$\phi =-\frac{i\ln(\frac{i\left(\sqrt{r^{2}-9}+r\right)}{3})}{3}+\frac{2\pi n_{1}}{3}\text{, }n_{1}\in \mathrm{Z}$$

$$\phi =-\frac{i\ln(\frac{-i\sqrt{r^{2}-9}+ir}{3})}{3}+\frac{2\pi n_{2}}{3}\text{, }n_{2}\in \mathrm{Z}$$

Trova r

$$r=3\sin(3\phi )$$

Trova φ

$$\phi =\frac{\arcsin(\frac{r}{3})+2\pi n_{1}}{3}\text{, }n_{1}\in \mathrm{Z}$$

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