Question

Question #2d31f

Answer 1

Explanation:

I presume you mean the function `sin(ceil(x))`, where `ceil(x)` denotes the next integer greater than or equal to `x`.

Then, define `f(x)=sin(ceil(x))`.

For any `x` such that `0<x<1`, `f(x)=sin(1)~~0.841`.
Similarly, for any `x` such that `1<x<2`, `f(x)=sin(2)~~0.909`.

Then, for `n<x<n+1` then `f(x)=sin(n)` for `n in Z`. The function is essentially constant on the intervals between integer values of `x` with jump discontinuities at `n` such that `n in Z`.