how does one find the period of this function
$\displaystyle y(x)=sin\frac{8\pi x}{9} cos\frac{3\pi x}{4}$
Ah yes.
$\displaystyle
sin\frac{8\pi x}{9} cos\frac{3\pi x}{4}= \frac {\sin (-7 x \pi /20) + \sin (17 x \pi /20)} 2
$
So the frequency of each sine wave can be found...
$\displaystyle
f_1=7/40
$
$\displaystyle
f_2=17/40
$
And to find the fundamental frequency...
$\displaystyle
f_o=GCD(7/40,17/40)=1/40
$
Which gives a period of...
$\displaystyle
T_o=40
$