Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A very weird problem

  1. Sep 24, 2006 #1
    what would be the period of cos(2pi*x)*sin(2pi*x)??
    calculator is telling me it's 2, but i somehow dont wanna believe that

    also, what would be the period of cos(2pi*m*x)*sin(2pi*m*x)??
  2. jcsd
  3. Sep 24, 2006 #2


    User Avatar

    [tex]cos 2\pi x sin 2\pi x = \frac{1}{2}sin 4\pi x[/tex],
    so the period is [tex]\frac{4\pi}{2\pi} = 2[/tex]
  4. Sep 24, 2006 #3
    That's almost correct, but the period is 1/2: if x increases from 0 to 1/2, then [tex] 4 \pi x[/tex] increases from 0 to [tex]2 \pi[/tex].
  5. Sep 24, 2006 #4
    As a rule, the period of sin(n*x) or cos(n*x) is 2*pi/n. More generally, if f(x) is a periodic function with period T, than f(n*x) has period T/n. You can deduce this simply by thinking that when you multiply the argument of a periodic function by a number you actually multiply its speed of oscillation by that number, meaning that you divide its period by that number.
    So the period of cos(2pi*x) is 1. The same for sin(2pi*x). To calculate the period of cos(2pi*x)*sin(2pi*x) you can write these two functions in the complex form and see that their product has the same period as cos(4pi*x) which is 0.5. Do the same for cos(2pi*m*x)*sin(2pi*m*x).
    Last edited: Sep 24, 2006
  6. Sep 24, 2006 #5


    User Avatar

    You're right
  7. Sep 24, 2006 #6
    i agree with you people that the period should be 1/2.
    but when i look at the graph, it seems like it's 2!
    can anybody plot for me and see if they are getting the period 1/2 or 2, just based on the plot?
  8. Sep 25, 2006 #7


    User Avatar
    Staff Emeritus
    Science Advisor

    I graphed it on a TI 93 and it looks to me like the period is clearly 1/2. Of course, since 2 is a multiple of 1/2, 2 is a period.
  9. Sep 25, 2006 #8


    User Avatar

    Here is a plot.

    Attached Files:

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: A very weird problem
  1. A weird little problem (Replies: 1)

  2. A weird math problem (Replies: 8)

  3. Very cool problem (Replies: 11)