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Math Help - sin 2x - sin x/2

  1. #1
    Senior Member Twig's Avatar
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    sin 2x - sin x/2

    Hi!


    Itīs been some time since I last did trigonometric equations.
    I dont remember if I should know this or not, but anyway, right now I dont.

    f(x)= sin 2x - sin x/2 is periodic with what period?

    Just point me in a direction, thanks!
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  2. #2
    Moo
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    Hello,

    We know that sinus is 2pi-periodic.

    sin(X+2pi)=sin(X)

    sin(2x) -> find t such as sin(2(x+t))=sin(2x)
    sin(2(x+t))=sin(2x+2t)=sin(2x)

    This means that 2t=2pi -> t=pi

    Do the same for sin(x/2) and finding t' such as sin((x+t')/2)=sin(x/2)

    The period of the function will be gcd(t,t')
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  3. #3
    Senior Member Twig's Avatar
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    I dont get it, pretty much nothing =)
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  4. #4
    Moo
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    Well, i'm sorry, i really can't explain more :'(
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  5. #5
    Senior Member Twig's Avatar
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    hi

    Well...

    sin x -> sin (x + n*2pi) where n is a whole number

    so sin 2x -> sin 2(x + n*2pi) correct?

    gives -> sin (2x + n*4pi) correct?

    so sin 2x is periodic with 4pi?
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  6. #6
    Moo
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    No, you can't...

    so sin 2x -> sin 2(x + n*2pi)
    What does that mean ?

    The periodicity of a function is defined as : h(x+t)=h(x)

    Suppose that f(x)=sin(x) and g(x)=2x

    Here, sin(2x)=f(g(x))=h(x)

    So you have to find t such as h(x+t)=h(x)

    If you replace, it makes : \underbrace{f(g(x+t))}_{\sin(2(x+t))}=\underbrace{  f(g(x))}_{\sin(2x)}

    So you have to find t as i told you above : such as \sin(2x+2t)=\sin(2x)

    sin(2x+2pi)=sin(2x)

    So t=pi works
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  7. #7
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Moo View Post
    Hello,

    We know that sinus is 2pi-periodic.

    sin(X+2pi)=sin(X)

    sin(2x) -> find t such as sin(2(x+t))=sin(2x)
    sin(2(x+t))=sin(2x+2t)=sin(2x)

    This means that 2t=2pi -> t=pi

    Do the same for sin(x/2) and finding t' such as sin((x+t')/2)=sin(x/2)

    The period of the function will be gcd(t,t')
    very nice method... by the way, it is "sine" not "sinus"
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  8. #8
    Moo
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    Grmbl !
    Ok, one more thing to learn ^^
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