Thread: period two product of sin, cos

1. period two product of sin, cos

how does one find the period of this function

$y(x)=sin\frac{8\pi x}{9} cos\frac{3\pi x}{4}$

2. Originally Posted by jut
how does one find the period of this function

$y(x)=sin\frac{8\pi x}{9} cos\frac{3\pi x}{4}$
Try using the identity $\sin A \cos B = \frac {\sin (A-B) + \sin (A+B)} 2$

and see where that takes you.

3. Ah yes.

$

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...

$
f_1=7/40
$

$
f_2=17/40
$

And to find the fundamental frequency...

$
f_o=GCD(7/40,17/40)=1/40
$

Which gives a period of...

$
T_o=40
$