## Calculus (3rd Edition)

Assume that $f(x)= x-\cos x$, then we show that $f(x)$ has a zero $[0,1]$. Indeed, since the function $f(x)=x-\cos x$ is continuous on $[0,1]$ and $f(0)=-1 <0$ and $f(1)=1 -\cos 1 > 0$ then by the bisection method $f(x)$ has a zero in the interval $(0,1)$. Hence $x=\cos x$ has a solution in $[0,1]$.