Value of sin infinity
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See, first of all, infinity is not a value, as we say 1, 2/7, π etc, these all are well-defined values but infinity is not so.
It is just a symbol, the way we define infinity is just to say that it goes on the positive side, that means it is something which is bigger than any real value.
As we know the nature of the sin function is periodic and it takes each and every value between -1 to 1.
We can't get a unique answer even if x take bigger and bigger values.
Nature will remain the same.
Which contradicts the fact that if the limit exists then it is unique, so that limit doesn't exist and so we can say that the sin infinity doesn't exist.
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