Graph a function $|\frac{\sin x}{x}|$

Question

How can one graph a function $\left|\frac{\sin x}{x}\right|$, $x\neq0$ without any program by hand? Without using derivatives.

Answer 1

hint

The function is even.

You begin by the graph $ C $ of $ \; x\mapsto \frac{\sin(x)}{x} $ at $(0,+\infty) $ and then its absolute value.

You know that

$$(\forall x>0)\;\; -\frac 1x\le \frac{\sin(x)}{x}\le \frac 1x$$

So, the graph $ C $ oscillates between the two hyperbolas whose equations are $ y=\pm \frac 1x$.

they intersect at $ x $ satisfying

$$\sin(x)=\pm 1$$ or $$x=\frac{\pi}{2}+k\pi$$