sin(0)=0 requires to refer to the function definition.
sin(α) has been defined as:
Lets suppose that: alpha angle goes to zero (
α -> 0) and adjacent side is constant (
b = const).
It causes: opposite side goes to zero too (
a -> 0) and hypotenuse side goes to adjacent side (
h -> b). When angle is equal to
a is equal to
0 divided by
h is equal to
0. It means
sin(0) is equal to
0 acording to above definition.
Simple visualisation is presented on below picture: