Question

The period of the function $f\left(x\right)=\sin (x+3-[x+3])$, where $\left[\right]$ denotes the greatest integer function is

• A. $2\pi +3$
• B. $2\pi$
• C. $1$
• D. $3$

Answer 1

The correct option is C $1$

$f\left(x\right)=\sin (x+3-[x+3])=\sin (x+3-[x]-3)=\sin (x-[x\left]\right)=\sin \left\{x\right\}$
we know the period of $\left\{x\right\}$ is $1$. Hence period of given function is also $1$