(UFGO) trigonometry The set of all values ​​of $x$, so that the angle
$\left(\frac{x}{x^{2}+1}\right)\pi\,$ rad belongs to the $1^\mathrm{st}$ quadrant, is represented by what interval?
This is an inequality that I did for 
$\frac{x}{x^{2}+1}π≤\frac{π}{2}$
$\frac{x}{x^{2}+1}-\frac{1}{2}≤0$  then $\frac{-x^{2}+2x-1}{2x^{2}+1}≤0$ and what now?
Answer: $\;\left] 0;1\right[ \cup \left]1;+\infty\right[$

HINT Angle $\theta$ belongs to the first quadrant is the same as $\,0\le \theta\le \dfrac{\pi}{2},$ i.e.
$$
0\le\left(\frac{x}{x^{2}+1}\right)\pi\le\frac{\pi}{2} \quad
\implies
\quad 0\le\frac{x}{x^{2}+1}\le\frac{1}{2} \quad
\iff\quad
\left\lbrace\begin{align}
\frac{x}{x^{2}+1} &\ge 0, &\text{and} \\
\frac{x}{x^{2}+1}&\le \frac{1}{2}.
\end{align}\right.
$$
Can you find all values of $x$ which satsfy two inequalities above?
