Answer
The function will be periodic, if it repeats its character after a certain interval of time.
That is, if $f\left( x+T \right)=f\left( x \right)$
then it will be a periodic function.
Work Step by Step
Sine and cosine functions are periodic because they repeat their character after $2\pi $ , or
$\begin{align}
& \sin \left( x+2\pi \right)=\sin x \\
& \cos \left( x+2\pi \right)=\cos x \\
\end{align}$
So, the sine and cosine functions are periodic.
Example:
$\begin{align}
& \sin \left( \frac{\pi }{4}+2\pi \right)=\sin \frac{\pi }{4} \\
& \cos \left( \frac{\pi }{4}+2\pi \right)=\cos \frac{\pi }{4} \\
\end{align}$
