How to find the intersection point between 2cosx and x/2

Question

I'm trying to find the solution to this because I need to find the area between the curves, but I need this intersection point to properly subtract the unnecessary parts.

I know how to do it with polynomials but with 2cosx and x/2 i just don't know what to do.

Thanks

Answer 1

You could use the fact that both function are continuous and the intermediate value theorem to approximate both intersection points with more "comfortable" numbers. As a start, note the following:

$$ x=-\pi, 2\cos x = -2 < \frac{x}{2}=-\frac{\pi}{2} $$ $$ x=0, 2\cos x=2 > \frac{x}{2}=0 $$ $$ x=\frac{\pi}{2}, 2\cos x = 0 < \frac{x}{2}=\frac{\pi}{4} $$