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Confusion with very basic algebra

  1. Sep 28, 2006 #1

    quasar987

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    I'm trying to find the points t in (0,2[itex]\pi[/itex]) such that sint=sin4t. So I use the fact that sinA=sinB <==> A=B+2n[itex]\pi[/itex] ([itex]n\in\mathbb{Z}[/itex]), which yields t=2n[itex]\pi[/itex]/3 ([itex]n\in\mathbb{Z}[/itex]). The only solutions of this in (0,2[itex]\pi[/itex]) are 2[itex]\pi[/itex]/3 and 4[itex]\pi[/itex]/3.

    However, there are 7 intersection points, says the "indirect method" of finding the zeros in (0,2[itex]\pi[/itex]) of sint-sin4t = sint+sin(-4t) =2sin(3t/2)cos(5t/2).

    The number 7 is also confirmed by my calculator. So why doesn't the direct method using only the properties of sine, give the correct answer?!?! :confused:
     
    Last edited: Sep 28, 2006
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  3. Sep 28, 2006 #2

    StatusX

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    sinA=sinB <=> A=B+2npi or A=(2n+1)pi-B. Remember that sin(x) is periodic with period 2pi, but not one-to-one on a given period (ie, there are points within a single period with the same sin).
     
  4. Sep 28, 2006 #3

    quasar987

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    Hey, you're right! Thanks StatusX.
     
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