sin(4 pi t)+cos(7 pi t)
sin(0) = sin(2π), so as for the function sin(4πt) it will repeat itself when t = ½.
Think of when the function sin(4πt)+cos(7πt) will repeat itself.
Say you have two clocks with hands, one clock turning 4 rounds while the other turns 7 rounds.
You start the clocks simultaniously at a starting point = 0.
Now, how many rounds will the hand of clock A have to turn before the hands of both clocks meet in the starting position?
What question do you about this? Write it in terms of sin(x) and cos(x)? Determine its period and amplitude?
(Ah- the title of this thread says "find the period". It's always a bit iffy not to put the question in the body of the thread- careless people like me might not see it!)
Hello arif112. Welcome to PF.
I see that you're new here.
In the future, use the template that is provided for you when you start a new thread. Don't erase it, but fill it in.
Also, familiarize yourself with the rules for this forum. How to Ask for Homework Help
Include the entire question in the body of your initial post, It's not sufficient to post part (or all) of the question in the title and then leave that part out of the body .
You need to make an attempt at a solution.
Make an honest attempt. Show what you've tried. Discuss what you know about the problem and where you're stuck.
We can't help you if you don't give us information about your understanding of the problem.
For your problem, what is the period of each of the functions that you a given -- individually ?
A useful identity: sin((a+b)t)= sin(at)cos(bt)+ cos(at)sin(bt)
@arif112, please start a new thread with your question. Be sure to follow the advice that SammyS gave, about using the homework template and filling it in, as well as the information on how to ask a question in the link he provided.
Separate names with a comma.