Range of f(x)

[juantheron]

find range of

[math]f(x)=\frac{\sin^2 x+\sin x-1}{\sin^2 x-\sin x+2}[/math]

[BIT5]

[math] D \no{=} 0 \to \sin^2 x - \sin x + 2 \no{=} 0 [/math]

[math] \sin x = t [/math]

[math] t^2-t+2 \no{=} 0 \to t_{1,2} \no{=} \frac{\ \pm \sqrt{1-4}}{2} [/math]

siccome [math] \Delta