Solucionar y=1/5sinx+6cosx

$$y = \frac { 1 } { 5 \sin x + 6 \cos x }$$

Resolver para x (solución compleja)

$$x=2\pi n_{1}-i\ln(\frac{\left(\frac{6}{61}+\frac{5}{61}i\right)\left(\sqrt{1-61y^{2}}+1\right)}{y})\text{, }n_{1}\in \mathrm{Z}$$

$$x=2\pi n_{2}-i\ln(\frac{\left(-6-5i\right)\sqrt{1-61y^{2}}+\left(6+5i\right)}{y})+\ln(61)i\text{, }n_{2}\in \mathrm{Z}\text{, }y\neq 0$$

Resolver para y (solución compleja)

$$y=\frac{2}{\left(6-5i\right)e^{ix}+\left(6+5i\right)e^{-ix}}$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}+\pi -\arctan(\frac{6}{5})$$

Resolver para y

$$y=\frac{1}{5\sin(x)+6\cos(x)}$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}-\arcsin(\frac{6\sqrt{61}}{61})+\pi$$