Question

Show that the maximum and minimum values of
$8\cos \theta -15\sin \theta$ are $17$ and $-17$ respectively.

Answer 1

We know for $A\cos \theta +B\sin \theta +C$, the maximum value is $C+\sqrt{A^2+B^2}$ and the minimum value is $C-\sqrt{A^2+B^2}$

$\therefore$ for $8\cos \theta -15\sin \theta$,

A=8, B=-15 and C=0

Maximum value=$0+\sqrt{64+225}=17$

Mniimum value=$0-\sqrt{64+225}=-17$