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# The maximum and minimum values of $7\cos\theta+24\sin\theta$ are equal to

$(a)\;25\;and\;-25\qquad(b)\;24\;and\;-24\qquad(c)\;5\;and\;-5\qquad(d)\;None \;of\;these$

Can you answer this question?

We know that the maximum and minimum values of $a\cos\theta+b\cos\theta$ are $\sqrt{a^2+b^2}$ and $-\sqrt{a^2+b^2}$ respectively.
Hence,the maximum and minimum values of
$7\cos\theta+24\sin\theta$ are $\sqrt{7^2+{24}^2}=25$ and $-\sqrt{7^2+{24}^2}=-25$ respectively.
Hence (a) is the correct answer.
answered Oct 7, 2013