Question

Find the domains of definition of the following function:
$y=\frac{{\log }_8(x+1)}{{\sin }^{2}x-\sin x+0.25}.$

Answer 1

$y=\frac{{log}_8(x+1)}{{(sin}^{2}x-sinx+0.25)}=\frac{{log}_{8}x+1}{{(sinx-\frac{1}{2})}^2}$

$y$ must be real and finite.

Therefore, domain of $y$ is $x>-1$ and $\sin x\ne \frac{1}{2}$

Therefore, $x\in (-1,\infty )-\{n\Pi +(-1{)}^n\frac{\Pi }{6}\},n\in W$

$W$ is whole number.