Answer
$x=0.739$
Work Step by Step
Step 1. Let $f(x)=cos(x)-x$, we have $f(0)=cos(0)-0=1\gt0$ and $f(\pi/2)=cos(\pi/2)-\pi/2=-\pi/2\lt0$
Step 2. Based on the Intermediate Value Theorem, there will be a zero between $x=0$ and $x=\pi/2$.
Step 3. Graphing the function as shown, we can find a zero at $x=0.739$
