How do you find the period of y=1/2sin[(pix)/3]?

Apr 5, 2018

$\textcolor{b l u e}{6}$

Explanation:

If we express the the sine function in the form:

$y = a \sin \left(b x + c\right) + d$

Where:

$\boldsymbol{a} \setminus \setminus \setminus \setminus \setminus = \text{amplitude}$

$\boldsymbol{\frac{2 \pi}{b}} = \text{period}$

$\boldsymbol{\frac{- c}{b}} = \text{phase shift}$

$\setminus \setminus \setminus \setminus \boldsymbol{d} \setminus \setminus = \text{vertical shift}$

$y = \frac{1}{2} \sin \left(\frac{\pi}{3} x\right)$

$\therefore$

$b = \frac{\pi}{3}$

Period is:

$\frac{2 \pi}{b} = \frac{2 \pi}{\frac{\pi}{3}} = \frac{6 \pi}{\pi} = \textcolor{b l u e}{6}$

The graph confirms this: