calculus - Critical values of sine function, when undefined

This may be a beginner question, but I really want to understand this good and thorough.

I have this sine function, withing the interval $-3 ≤ x ≤ 3$

$$f(x)=\frac{\sin (\pi x)}{\sin(2\pi x)}$$

My question is regarding local maximum and minimum values wich i assume this function does not have, as all $f'(x)=0$ are undefined? In the same manner this function would also not have a horizontal tangent?

(as far as i understand its possible to transform the function using trig identities, but the questions above is regarding the function in it's original form.)

Would be really greatful for any help.