# How do you find the domain of f(x)=(x^2-4x+4)/(2sin(x))?

$f \left(x\right) = \frac{{x}^{2} - 4 x + 4}{2 \sin x} , x \in \mathbb{R} , x \ne n \pi$/$x \ne 180 n$
The domain of a function is all the values of $x$ for which the function is defined. Since the function is a quotient, the only values it isn't defined for is when the denominator is equal to zero.
Since the denominator is a $\sin$ function, we know that it will be equal to zero whenever $x$ is a multiple of ${\pi}^{\text{c}}$ or ${180}^{\text{o}}$. So we can write this as $x \ne n \pi$.