Question

$\text{Statement I}$: Period of $\sin x$ is $2\pi$.

$\text{Statement II}$: $P$ is period of $f\left(x\right)$ if $f(x+P)=f\left(x\right)$ for any value of $x$.

• A. I is true, II is true.
• B. I is true, II is false.
• C. Both I and II are false.
• D. I is false , II is true.

Answer 1

The correct option is A I is true, II is true.

Statement I: Period of $\sin x=2\pi$, which is true
Statement II: $p$ is a period of $f\left(x\right)$, if $f(n+p)=f\left(x\right)$ for any value of $x$.
$f(x+p)=f\left(x\right)$ for any $x$
e.g. $\sin x$ has a period of $2\pi$
which means $\sin (2\pi +\frac{\pi }{3})=\sin \frac{\pi }{3}=\frac{\sqrt{3}}{2}$