Number of roots Problem | TOMATO B.Stat Objective 712

The number of roots of the equation \(xsinx=1\) in the interval \([0,{2\pi}]\) is

\(f(x)=xsinx-1=0\)

which can be written as sinx=\(\frac{1}{x}\) and f(x) has solution at those points where sinx and \(\frac{1}{x}\) intersects

So let us draw the graph

here we see two graphs y=sin x and y=\(\frac{1}{x}\)

both graphs intersect at two points between \((0,2\pi]\)

or, number of roots is 2.

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