Question

Minimum value of $3\cos x+4\sin x$ is

• A. $-5$
• B. $9$
• C. $7$
• D. $3$

Answer 1

The correct option is A $-5$

As we know that

The range of $a\cos x+b\sin x+c$ is $[c-\sqrt{a^2+b^2},c+\sqrt{a^2+b^2}]$

Here $a=3,b=4,c=0$

So the range of $3\cos x+4\sin x$ is $[-\sqrt{3^2+4^2},\sqrt{3^2+4^2}]$

So the minimum value is $-\sqrt{3^2+4^2}=-5$