Question

The maximum value of the function $3\cos x-4\sin x$ is

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

The correct option is D

$5$

Explanation for the correct option:

Find the maximum value of the given trigonometric function.

A trigonometric function $3\cos x-4\sin x$ is given.

We know that, the maximum value of the function $a\cos x+b\sin x$ is given by $\sqrt{a^2+b^2}$.

Therefore, the maximum value of the given function is given by:

$$\begin{gathered} \sqrt{{\left(3\right)}^2+{(-4)}^2}=\sqrt{9+16} \\ \Rightarrow \sqrt{{\left(3\right)}^2+{(-4)}^2}=\sqrt{25} \\ \Rightarrow \sqrt{{\left(3\right)}^2+{(-4)}^2}=5 \end{gathered}$$

Therefore, the maximum value of $3\cos x-4\sin x$ is $5$.

Hence, the option $D$ is the correct answer.