Question

Find the number of solutions of $sinx=\left(\frac{x}{10}\right)$.

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Answer 1

Here,let $f\left(x\right)=sinxandg\left(x\right)=\frac{x}{10}$

Also we know; -1< sinx < 1

$\therefore$ -1< $\frac{x}{10}$$\le 1\Rightarrow -10$ < x <10

Thus,sketch both curves when $xϵ[-10,10]$

From above figure $f\left(x\right)=sinxandg\left(x\right)=\frac{x}{10}$ intersect at 7 points.so numbers of solutions is 7.