Does the limit exist

So I'm learning about limits of trigonometric functions in calculus and i came across a question that asked
find the limit.
lim sin 2y/15y
y->0

So, I know that you have to match the equation with
lim sinax/ax
x->0

and it matched so since lim y->0, i replaced the y with 0 and so
sin 2(0)/ 15(0) = 0

but im confused. Is the answer 0 or does the limit not exist?

lim(x--->0) sinax/ax = 1

lim (y--->0) sin 2y/15y = lim (y--->0) (2 * sin 2y)/(2*15y)

= lim (y--->0) (2 * (sin 2y)/2y * 1/15) = lim (y--->0) (2/15)(sin 2y)/2y

= 2/15 * 1 = 2/15

It's neither. The limit is 2/15. As given it doesn't match the form since 2 ≠ 15. You can do some trickery to make it fit, though, by saying that 15 = 2 * (15/2) so that we then have
(1 / (15/2)) lim[y->0] sin(2y) / (2y) = 2/15


I should also say that 0/0 ≠ 0, rather it's an indeterminate form.

sin(2y)/15y

= sin (2y)/2y * (2/15)

The first part of this is in the form sin(ay)/ay where a = 2. So the limit of the first term is 1, and so the limit of the whole expression is 2/15.