Is tan|x| periodic?


by Bassalisk
Tags: periodic, tan|x|
Bassalisk
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#1
Aug31-11, 05:59 PM
P: 951
Is tan|x| periodic and if not, why not?


I just found in my book that tan|x| isn't periodic, and how do we make up a rule how to seek periodicity of functions.

I.e.

ln(sin(x)), e^sin(x)... etc
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disregardthat
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#2
Aug31-11, 06:06 PM
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Find a constant a such that f(x+a) = f(x). So basically you can solve for a function a(x) here, and make sure its a constant function.
jambaugh
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#3
Aug31-11, 07:48 PM
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Plot the graph. Notice that if you erase the coordinate axes you can still see where the origin must lie.

Bassalisk
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#4
Sep1-11, 03:55 AM
P: 951

Is tan|x| periodic?


Quote Quote by jambaugh View Post
Plot the graph. Notice that if you erase the coordinate axes you can still see where the origin must lie.
I did plot the graph, thats why i got confused. I saw a lot of functions, resembling tan(x). I got the feeling that it was periodic, but actually tan|x| isn't.
jambaugh
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#5
Sep2-11, 07:08 AM
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Quote Quote by Bassalisk View Post
I did plot the graph, thats why i got confused. I saw a lot of functions, resembling tan(x). I got the feeling that it was periodic, but actually tan|x| isn't.
Look at the graph closely. It should have a mirror symmetry around x=0. But notice it is not mirror symmetric around any other point. So you can't shift the graph through a period so it looks exactly the same.
Bassalisk
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#6
Sep2-11, 07:36 AM
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Quote Quote by jambaugh View Post
Look at the graph closely. It should have a mirror symmetry around x=0. But notice it is not mirror symmetric around any other point. So you can't shift the graph through a period so it looks exactly the same.
Thank you I understand now. I had bad view of what it means to be periodic.


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