Question

Find the max. and min. value of
$7\cos \theta +24\sin \theta$

• A. $35$
• B. $25$
• C. $-25$
• D. $55$

Answer 1

Answer: (B), (C)

$-25$
$25$

In $7\cos \theta +24\sin \theta$
take $7=r\cos \alpha ;24=2\sin \alpha$
$\therefore r=\sqrt{7^2+{24}^2}=25$
LHS $=r(\cos \theta \cos \alpha +\sin \theta \sin \alpha )=25\cos (\theta -\alpha )$
Now max. and min. values of $\cos (\theta -\alpha )$ are $1$ and $-1$
Therefore max and min values of given expression are $25$ and $-25$