Periodic functions confusiom

If you just want to check your answer, go to desmos.com and graph all four functions, and see which look periodic.

If you want to do only what you can do by hand, then replace x with x+T and see whether you can manipulate f(x+T) to equal f(x), for some value(s) of T.
 
Cosx is surely periodic. Now if you keep taking ln of the same values, you will get the same results. Does this answer your concern.
 
Steven G said:
Cosx is surely periodic. Now if you keep taking ln of the same values, you will get the same results. Does this answer your concern.
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pretty much

Steven G said:
Cosx is surely periodic. Now if you keep taking ln of the same values, you will get the same results. Does this answer your concern.
Click to expand...
so is only ln(cosx) periodic from this list?
cos(lnx) isn't periodic, right???
 
Loki123 said:
lnx is not periodic, so i suppose cos(lnx) wouldn't be either, but i am not so sure.
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Good! So think about it until you satisfy everything in your mind. That means for the next hour or so you walk around and think about this very carefully.
 
Why is cos (x) periodic. Will changing x to ln x make cos(lnx) periodic. How about cos(4x)? cos(x+2)?
 
Steven G said:
Why is cos (x) periodic. Will changing x to ln x make cos(lnx) periodic. How about cos(4x)? cos(x+2)?
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cos4x is periodic Pi/2
cos(x+2) is periodic 2Pi
cos x repeats after 2Pi, that is, it is periodic 2Pi
i am not so sure if changing x to ln x will make a difference. I would suppose not.
 
Loki123 said:
lnx is not periodic, so i suppose cos(lnx) wouldn't be either, but i am not so sure.
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Loki123 said:
i am not so sure if changing x to ln x will make a difference. I would suppose not.
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What would it take to convince you? You should not be dependent on someone else telling you what's true; mathematics is not based on authority.

Would you like to use the definition of periodicity to prove it? Give it a try!

You might, for example, find when each function is zero, and see if those points are equally spaced (as they have to be if it is periodic).
 
Dr.Peterson said:
What would it take to convince you? You should not be dependent on someone else telling you what's true; mathematics is not based on authority.

Would you like to use the definition of periodicity to prove it? Give it a try!

You might, for example, find when each function is zero, and see if those points are equally spaced (as they have to be if it is periodic).
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I don't understand when a function is periodic or not. Especially when ln, log come into play.
 
Loki123 said:
I don't understand when a function is periodic or not. Especially when ln, log come into play.
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Please state the definition of a periodic function, as it was taught to you. (Or search for it.)

Then first try applying it to the cosine itself, then to one of the given functions.
 
Dr.Peterson said:
Please state the definition of a periodic function, as it was taught to you. (Or search for it.)

Then first try applying it to the cosine itself, then to one of the given functions.
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functions repeats after 2Pi, or Pi if it's ctg/tg
so 2Pi/B or Pi/B
B would be for example what it represents here Cos B(x+C)
 
Loki123 said:
functions repeats after 2Pi, or Pi if it's ctg/tg
so 2Pi/B or Pi/B
B would be for example what it represents here Cos B(x+C)
Click to expand...
That's not the definition; it's some examples, which have particular periods.

In general, a function f is periodic, with period T, if for any x, f(x+T) = f(x). In the case of sine or cosine, T is 2 pi; you show this by showing that cos(x + 2 pi) = cos(x).

So, what does ln(cos(x+T)) look like? What might T be?
 
Dr.Peterson said:
That's not the definition; it's some examples, which have particular periods.

In general, a function f is periodic, with period T, if for any x, f(x+T) = f(x). In the case of sine or cosine, T is 2 pi; you show this by showing that cos(x + 2 pi) = cos(x).

So, what does ln(cos(x+T)) look like? What might T be?
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i know this might be difficult to believe, but my mind is blank
 
If you compute ln of the same value you obviously get the same result. That is ln(.6) = ln(.6)

Now cos(x+2pi) = cos(x), so ln(cos(x+2pi)) = ln(cos(x)). So ln(cosx) is periodic.

Try the same for cos(lnx).
 
Steven G said:
If you compute ln of the same value you obviously get the same result. That is ln(.6) = ln(.6)

Now cos(x+2pi) = cos(x), so ln(cos(x+2pi)) = ln(cos(x)). So ln(cosx) is periodic.

Try the same for cos(lnx).
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cos(ln(x+2pi)) i don't know how to turn that to cos(ln(x))
 
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