What is the fundamental period of the function f(t)= sin6t + cos8t?

[Luongo]

1. what's the fund. period of f(t)= sin6t + cos8t?
2. the fund period of the first term is pi/3, the second pi/4
3. do i just add the 2 fundamental periods up to get the whole fund period? also for the Fourier coefficients of this function, should i use euler's to make it into exponentials before i integrate to avoid by parts method? or just integrate as is.

 

[fzero]

What is the definition of the fundamental period? Does the sum of pi/3 and pi/4 satisfy the definition?

 

[Luongo]

What is the definition of the fundamental period? Does the sum of pi/3 and pi/4 satisfy the definition?

you're just asking me what I'm asking you in other words
im not sure. the fund freq is the smallest period for the function and pi/3 and pi/4 are those... summed right

 

[fzero]

I'm asking you because you don't seem to understand the definition and that's where we need to start to do this problem. The (fundamental) period of a function is the smallest value of T such that f(t+T) = f(t). You should verify that your guess doesn't satisfy this.

It's unnecessary to try to guess at solutions. You can use the trig sum of angle formulas to solve this equation explicitly. Otherwise you have to know something about common multiples.

 

[Luongo]

I'm asking you because you don't seem to understand the definition and that's where we need to start to do this problem. The (fundamental) period of a function is the smallest value of T such that f(t+T) = f(t). You should verify that your guess doesn't satisfy this.

It's unnecessary to try to guess at solutions. You can use the trig sum of angle formulas to solve this equation explicitly. Otherwise you have to know something about common multiples.

can you save me the misery and tell me what it is? i work better once i have the solution is it pi?

 

[fzero]

can you save me the misery and tell me what it is? i work better once i have the solution is it pi?

It would be unethical (and against the forum rules) to give the answer away when you won't attempt to work on the problem for yourself.

 

[Luongo]

the smallest period for both is PI. thus PI should be the fund period of the sum of the two is this logic right/

 

[jas44]

I have the same question and I know the fundamental period is the smallest period of a function. So if we break apart the function f(x) we know that sin(6t) has a fundamental period of pi/3 and for cos(8t) the fundamental period is pi/4. I'm not quite sure how we can add these and i tried simplifying using identies but didn't get anywhere. What should be my next step?