Question

The fundamental period of the function $f\left(x\right)=3+2\sin \left\{\frac{(\pi x+2)}{3}\right\}$ is

Answer 1

We have,
$f\left(x\right)=3+2\sin \left\{\frac{(\pi x+2)}{3}\right\}$
Rearranging, we get
$f\left(x\right)=3+2\sin \{\frac{\pi }{3}x+\frac{2}{3}\}$
The period of $\sin$ function is $2\pi .$
The given function is of the form $af(bx+c)+d.$
Hence, the fundamental period of $f\left(x\right)$
$=\frac{2\pi }{|b|}=\frac{2\pi }{\frac{\pi }{3}}=6$