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Math Help - f(x)=3sin x+4sin(x-3)

  1. #1
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    f(x)=3sin x+4sin(x-3)

    For these I'm clueless. Please help

    1) If f(x)=3sin x+4sin(x-3) what is the amplitude and period (p) of f(x)?
    A) a= 1.114, p = 6.283
    B) a= 1.114, p = 3.141
    C) a =2.28, p= 3.141
    D) a=7, p = 6.283
    E) a= 7, p= 9.425
    Last edited by mr fantastic; April 23rd 2011 at 12:46 AM. Reason: Moved from another thread.
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  2. #2
    Senior Member abhishekkgp's Avatar
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    Quote Originally Posted by pcalhelp View Post
    I got a bunch of homework. But these are the hardest. Others I could have some clues to solve, but for these I'm clueless. Please help

    1) If f(x)=3sin x+4sin(x-3) what is the amplitude and period (p) of f(x)?
    A) a= 1.114, p = 6.283
    B) a= 1.114, p = 3.141
    C) a =2.28, p= 3.141
    D) a=7, p = 6.283
    E) a= 7, p= 9.425
    use sin(x-3)= sin(x)cos(3)-cos(x)sin(3).
    then f(x) takes the form p(sinx) + q(cosx).
    its maximum value is sqrt(p^2+q^2).

    to see this let sqrt(p^2+q^2)=k
    then f(x)=p(sinx)+q(cosx)= k[(p/k)(sinx)+ (q/k)(cosx)].
    observe that p/k can be taken as cos of some angle say 'y' so p/k=cosy.
    this forces q/k=siny.

    f(x)= k[(cosy)(sinx)+(siny)(cosx)]= k(sin(x+y)). clearly its maximum is k.
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