limits - How I can solve: $lim_{(x,y) rightarrow (0,0)} acosleft(frac{x}{sqrt{x^2+y^2}}right)$

$$\lim_{(x,y) \rightarrow (0,0)} a\cos\left(\frac{x}{\sqrt{x^2+y^2}}\right)$$ Hi, could someone explain to me how I can solve that limits, i thought that i could studying $L_2=\lim_{(x,y) \rightarrow (0,0)} \frac{x}{\sqrt{x^2+y^2}}$ and do $a\cos(L_2)$, but I dont know if this way it is correct, thanks

Answer

HINT:

Tranform to polar coordinates with $x=\rho \cos \phi$ and $y=\rho \sin \phi$. Then $\sqrt{x^2+y^2}=\rho$.