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What is the limit sin∞?
Sine and cosine functions are bounded,

Definition of positive metaphysics

It is only the ratio of the side to the hypotenuse corresponding to an acute angle in a right triangle. According to the relationship between the three sides of a right triangle, it is easy to know that the right side can never be larger than the hypotenuse, so the maximum value of the sin function is infinitely close to 1.

When there is no specific value because of infinity, the value of sin can only fluctuate from 0 to 1.