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How can we graphically show an anti-periodic function? I can't imagine. Maybe I have got no imagination...!! for example we can show the sin and cos or other periodic functions on the graphs. is it the possible for an anti-periodic one?

P.A.M
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1 Answers1

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$f(x+p)=-f(x)$ then its anti-periodic

(to see intuitively graphically its like an odd function which is also periodic )

all anti-periodic functions with period $p$ are periodic with period $2p$

not all periodic functions have corresponding anti-periodic function

but all anti-periodic functions are periodic

it is enough to show that your function is periodic and odd with when shifted by half of the period.

example http://www.wolframalpha.com/input/?i=sin%28x%2Bpi%29

$sinx$ is periodic with $2\pi$ period so you check if $sin(x+\pi)=-sinx$ if it is then its anti-periodic with period $\pi$

Mr. Math
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  • i think there is a miss definition of periodicity here. because we say: it is anti-periodic in period ... . or we can say: really we don't have an anti-periodic function and we define some periodic functions in some intervals as anti-periodic.!!? – P.A.M Dec 17 '14 at 13:53
  • @P.A.M unfortunately its how its defined the language used in maths sometimes is confusing here anti-period implies its the same value except its opposite sign of the original value http://mathworld.wolfram.com/AntiperiodicFunction.html – Mr. Math Dec 17 '14 at 13:55
  • perhaps it should be called periodic reflection on x-axis but the name anti-periodic is being used for some reason – Mr. Math Dec 17 '14 at 13:57
  • although it sounds right but i can't imagine it boy. :) i think we don't have anti-periodicity of a real function. – P.A.M Dec 17 '14 at 14:01
  • technically for any real valued function in interval we can assume it is anti-periodic with period as the size of interval – Mr. Math Dec 17 '14 at 14:04
  • here, is sin(x+pi) anti-periodic or is sin(x) anti-periodic in an interval ? – P.A.M Dec 17 '14 at 14:08
  • $sin(x+\pi)$ is anti periodic with period $\pi$ and also periodic with period $2\pi$ – Mr. Math Dec 17 '14 at 14:09
  • then, it should be so that: sin(x+pi) is anti-periodic compared to the sin(x). not compared to itself!! – P.A.M Dec 17 '14 at 14:14