Mathematics

The key is the Intermediate Value Theorem: since $f(x) = \cos x$ is continuous and decreases from $f(0) = 1$ to $f(\pi/2) = 0$ on $[0, \pi/2]$, while $g(x) = 0.3$ is a horizontal line, you just need to check whether $0.3$ lies between the endpoint values. If it does, the curves must intersect at least once.

The key is the Intermediate Value Theorem: since $f(x) = \cos x$ is continuous and decreases from $f(0) = 1$ to $f(\pi/2) = 0$ on $[0, \pi/2]$, while $g(x) = 0.3$ is a horizontal line, you just need to check whether $0.3$ lies between the endpoint values. If it does, the curves must intersect at least once.