Write the function `f(x) ={sinx}` where {.} denotes the fractional part function) in piecewise definition.

Explanation

We have `f(x)={sinx}`
Clearly, `{sinx}=0` if sin x is integer.
` :. {sinx}=0 " when " x=(n pi)/(2)`
Now when ` sin x in (0,1)`
` {sin x} =sin x-[sin x]=sin x -0=sinx`
When ` sinx in (-1,0),`
` {sin x} =sin x-[sin x]=sin x -(-1)=sinx+1`
Thus, `f(x)={(0","sinx in{-1,0,1}),(sinx","sinx in (0,1)),(sinx+1","sinx in (-1,0)):}`
`f(x)={(0",",x=(n pi)/(2)","n in Z),(sinx",",x in underset(n in Z)(cup)(2n pi","(2n+1)pi)),(sinx+1",",x in underset(n in Z)(cup)"((2n+1)"pi","(2n+2)pi")"):}`