period two product of sin, cos

**jut** · October 7th 2009, 10:20 PM

how does one find the period of this function

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

**Matt Westwood** · October 7th 2009, 10:24 PM

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.

**jut** · October 7th 2009, 11:05 PM

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 $

Thread: period two product of sin, cos

LinkBack

Thread Tools

Display

period two product of sin, cos

Similar Math Help Forum Discussions

what is the period

sin(x), sin(2x), sin(1/2)....what is the period?

[SOLVED] Future value annuities with a different payment period to the compounding period.

Period : 2

Period

Search Tags