In mathematics, the sine and cosine functions are defined for all real numbers. However, when we talk about the value of these functions at infinity, it brings us to interesting characteristics of periodic functions.
The sine function, sin(x), oscillates between -1 and 1 for all values of x. Similarly, the cosine function, cos(x), also oscillates between -1 and 1. This means that as x approaches infinity, sin(x) and cos(x) do not settle at a specific value but continue to vary endlessly.
To summarize, the values of sin(∞) and cos(∞) are undefined in the traditional sense as they do not converge to a single value. Instead, they remain periodic, bouncing between their maximum and minimum values of -1 and 1.