Question

The maximum 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 $5$

Let $y=3\cos x-4\sin x$

$\therefore y_{max}=\sqrt{3^2+4^2}=5$

Note: $-\sqrt{a^2+b^2}\le a\sin x+b\cos x\le \sqrt{a^2+b^2}$