find n

\frac{sin x^n}{x}=x^{n-1}\times\frac{sin x^n}{x^n}

For this to be finite or well defined n has to be 1
if n is greater than 1 the limit is zero
if it is less than 1 it does not exist...
When n is 1, this limit is 1 not pi/180

The problem is that there should have been x° at one place...
Please see the question again..

Otherwise the answer will be there is no value of n