Question

Find the number of solutions of $\sin x=\frac{x}{10}$

Answer 1

Here, let $f\left(x\right)=\sin x$ and $g\left(x\right)=\frac{x}{10}$. Also, we know that $-1\le \sin x\le 1$
$\Rightarrow$ $-1\le \frac{x}{10}$ or $-10\le x\le 10$
Thus, sketch both curves when $xϵ[-10,10]$
From Fig, $f\left(x\right)=\sin x$ and $g\left(x\right)=\frac{x}{10}$ intersect at seven points. So, the number of solutions is seven.
Ans: 7