calculus - Evaluating $lim_{x to 0}{frac{sin(4x)}{sin(3x)}}$ without L'Hospital

I need to evaluate
$$\lim_{x \to 0}{\frac{\sin(4x)}{\sin(3x)}}$$
I solved this using L'Hospital's Theorem and I got 4/3
However, is there a way to do this without applying this theoerm?

Answer

As $$\lim_{x \to 0}\frac{\sin(x)}{x}=1$$
$$\lim_{x \to 0}{\frac{\sin(4x)}{\sin(3x)}}$$ can be written as
$$
\frac{4}{3}\lim_{x \to 0}\frac{\sin(4x)}{4x}\frac{3x}{\sin(3x)}
$$
$$=\frac{4}{3}$$