A student claims that the maximum of$$h(x)=3\sin x+4\cos x,\qquad 0^\circ\le x\le30^\circ,$$ is \(5\

Question

A student claims that the maximum of$$h(x)=3\sin x+4\cos x,\qquad 0^\circ\le x\le30^\circ,$$ is $5$. Explain why this claim is incorrect. Find the actual maximum and minimum, giving exact values and the corresponding values of $x$.

Accepted Answer

Maximum $(3+4\sqrt3)/2$ at $30^\circ$; minimum $4$ at $0^\circ$; $5$ is unattainable.

Trigonometry

Trigonometry