Big O Notation

I have been given the following problem

Are the following statements true or false? If a statement is true specify a constant C and a threshold t0 fulfilling the definitions of the Big O notation.

(a) sin x = O(1) as x tend to infinity

The constant C is obviously 1 in this case however I am not sure what the threshold should be

As far as I can see this applies for all x so can I say t0 = negative infinity? Or is it acceptable to select any t0 for which the relationship holds. Such as t0 = 0?