Question

Solve the following inequalities.
Find the maximum value of the function $f\left(x\right)=3sinx+4cosx.$

Answer 1

We know that the maximum value of the function of the form

$a\sin x+b\cos x$ is $\sqrt{a^2+b^2}$ and the minimum value is $-\sqrt{a^2+b^2}$

Here, the maximum value of $f\left(x\right)=3\sin x+4\cos x$ is-

$f_{max}\left(x\right)=\sqrt{3^2+4^2}=5$