Resolver sinx=2/3,pi/2leqθleqpi,text{entoncescot}θ

$$\sin x = \frac { 2 } { 3 } , \pi / 2 \leq \theta \leq \pi , \text { entonces cot } \theta$$

Ebatzi: x

$$x\in 2\pi n_{1}+\arcsin(\frac{2}{3}),2\pi n_{1}+\pi -\arcsin(\frac{2}{3})$$

$$n_{1}\in \mathrm{Z}$$

$$\theta \geq \frac{\pi }{2}$$

Ebatzi: θ

$$\theta \geq \frac{\pi }{2}$$

$$\exists n_{2}\in \mathrm{Z}\text{ : }x=2\pi n_{2}+\pi -\arcsin(\frac{2}{3})\text{ or }\exists n_{1}\in \mathrm{Z}\text{ : }x=2\pi n_{1}+\arcsin(\frac{2}{3})$$