Question

Find maximum and minimum value of -2 + 7Cos theta - 24Sin theta​

Answer 1

Answer:

because I am single I am happy

Answer 2

Step-by-step explanation:

Let $y=-2+7\cos(\theta)-24\sin(\theta)$

$\implies \: y = 25 \bigg \{ \frac{7}{25} \cos( \theta) - \frac{24}{25} \sin( \theta) \bigg \} - 2$

$\implies \: y = 25 \bigg \{ \sin( \alpha ) \cos( \theta) - \cos( \alpha ) \sin( \theta) \bigg \} - 2$

Where, $\alpha=\tan^{-1}\bigg(\frac{7}{24}\bigg)$

So,

$\implies \: y = 25 \sin( \alpha - \theta) - 2$

We know, $-1\leqslant\sin(x)\leqslant1$

So,

$- 1 \leqslant \sin( \alpha - \theta) \leqslant 1$

$\implies \: - 25 \leqslant 25\sin( \alpha - \theta) \leqslant 25$

$\implies \: - 25 - 2 \leqslant 25\sin( \alpha - \theta) - 2 \leqslant 25 - 2$

$\implies \: - 27 \leqslant y \leqslant 23$

$\tt \bold{ Hence \: \: the \: \: maximum \: \: and \: \: minimum}\\ \bold{values \: \: of \: \: the \: \: given \: \: expression}\\ \bold{ are \: \: - 27 \: \: and \: \: 23 \: \: respectively }$