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    Hexial's Avatar
    Hexial Posts: 7, Reputation: 1
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    #1

    May 6, 2009, 09:46 AM
    solve sin(2x)=1/2
    I really don't know, can someone help me...
    Capuchin's Avatar
    Capuchin Posts: 5,255, Reputation: 656
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    #2

    May 6, 2009, 10:08 AM

    simple algebra:







    This will give you the lowest value of x. You need to remember that there are in fact an infinite number of values for x, as the graph at the bopttom of the post shows. Each of my lines shows the positions of solutions to sin(2x) = 1/2 between 0 and 10. Working them out should be fairly trivial.

    Let me know if you need more help!
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    Hexial's Avatar
    Hexial Posts: 7, Reputation: 1
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    #3

    May 6, 2009, 10:37 AM
    Quote Originally Posted by Capuchin View Post
    simple algebra:







    This will give you the lowest value of x. You need to remember that there are in fact an infinite number of values for x, as the graph at the bopttom of the post shows. Each of my lines shows the positions of solutions to sin(2x) = 1/2 between 0 and 10. Working them out should be fairly trivial.

    Let me know if you need more help!
    you insane?? You can't multiply or divide with sin!!

    this is the solution

    sin(2x)=1/2

    {sin(30°)=1/2}

    sin(2x)=sin(30°)
    2x=30°
    x=15°
    Hexial's Avatar
    Hexial Posts: 7, Reputation: 1
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    #4

    May 6, 2009, 10:40 AM

    Graphic side is OK, but nul points aren't asigned so I can only assume what are they
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    Unknown008 Posts: 8,076, Reputation: 723
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    #5

    May 6, 2009, 10:44 AM
    Quote Originally Posted by Hexial View Post
    you insane??? you can't multiply or divide with sin!!!

    this is the solution

    sin(2x)=1/2

    {sin(30°)=1/2}

    sin(2x)=sin(30°)
    2x=30°
    x=15°
    Hey, be polite at least!:mad: Some people are trying to help, and they may have their own methods. You don't have to criticize other's methods, since you yourself couldn't solve the problem earlier.
    Capuchin's Avatar
    Capuchin Posts: 5,255, Reputation: 656
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    #6

    May 6, 2009, 10:57 AM

    I wasn't dividing by sin, i was using the inverse sin operator on both sides, where . This is perfectly acceptable, and all scientific calculators have this function.

    Also, the graph wasn't for you to read off the answer, it was to show you that there are an infinite number of values of 2x. Your answer gives only one of them (and i point out that your solution is the same as mine!).
    Hexial's Avatar
    Hexial Posts: 7, Reputation: 1
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    #7

    May 6, 2009, 02:13 PM
    Quote Originally Posted by Unknown008 View Post
    Hey, be polite at least!:mad: Some people are trying to help, and they may have their own methods. You don't have to criticize other's methods, since you yourself couldn't solve the problem earlier.
    True... my apologies, I bumped into the solution after some time...
    Hexial's Avatar
    Hexial Posts: 7, Reputation: 1
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    #8

    May 6, 2009, 02:16 PM
    Quote Originally Posted by Capuchin View Post
    I wasn't dividing by sin, i was using the inverse sin operator on both sides, where . This is perfectly acceptable, and all scientific calculators have this function.

    Also, the graph wasn't for you to read off the answer, it was to show you that there are an infinite number of values of 2x. Your answer gives only one of them (and i point out that your solution is the same as mine!).
    so you're saying that [ sin(x) / sinx ] = x? Don't know man, this is the fist time i see smth like this...
    Hexial's Avatar
    Hexial Posts: 7, Reputation: 1
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    #9

    May 6, 2009, 02:17 PM

    [ sin(x) / sin ] =x

    sorry, not used to write sin all alone...
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    Hexial Posts: 7, Reputation: 1
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    #10

    May 6, 2009, 02:46 PM

    you used the arc function... sin^(-1) = arc



    I used the same function in my 3rd step...
    both our solutions are correct...

    and I would like to apologise to you for calling you insane, sorry ,)...
    Capuchin's Avatar
    Capuchin Posts: 5,255, Reputation: 656
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    #11

    May 6, 2009, 03:49 PM

    generally, ^(-1) of a function implies the inverse of the function. For example if f(x) = 2(x^2) then f^-1(x) = (1/2x)^0.5. not simply 1/f(x)

    You need to recognise the other solutions, x=pi/12 isn't the only answer. You don't have a complete solution yet.

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