# Question #47e3f

Dec 5, 2016

We know that $- 1 \le \cos \theta \le 1$

when $\theta = \left(2 n + 1\right) \pi , \cos \theta = - 1$
and when $\theta = 2 n \pi , \cos \theta = 1$
$\text{ where } n \in \mathbb{Z}$

So maximum value of $\cos \left(5 x\right) = 1$ and minimum value of $\cos \left(5 x\right) = - 1$

Hence

${Y}_{\text{max}} = 10 \cdot 1 - 1 = 9$

${Y}_{\text{min}} = 10 \cdot \left(- 1\right) - 1 = - 11$