# Question #4fe1b

Aug 28, 2016

Given equation can be written as

$6 \sin \left(\frac{\pi}{12} \left(x - 11\right)\right) + 19 = 19$

$\implies 6 \sin \left(\frac{\pi}{12} \left(x - 11\right)\right) = 19 - 19 = 0$

$\implies \sin \left(\frac{\pi}{12} \left(x - 11\right)\right) = \frac{0}{6} = 0$

$\implies \left(\frac{\pi}{12} \left(x - 11\right)\right) = n \pi$,$\text{ where } n \in \mathbb{Z}$

$\therefore x = 12 n + 11$$\text{ where } n \in \mathbb{Z}$