Do you mean the tangentline?In order for a graph to have a tangent line at a point, it needs to bedifferentiableat that point. This means that the derivative will exist.

We could use derivative rules to find the derivative of that function and see whether it exists or not, but in this case its simpler to use the limit definition of derivative at a point.

Now to see that this limit is undefined, notice that the graph will oscillate infinitely faster and faster as x approaches 0. To see this, make the substitution x = 1/y. So as x approaches 0 from the right, y approaches infinity, since 1/0 gets larger and larger.

And this is undefined due to the oscillating nature of the sine function. Thus the limit does not exist, the derivative is undefined, and there is no tangent line.