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Thread: [Resolved] Sum Identity

  1. Nov 26th, 2002, 09:44 PM #1
    The Hobo
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    [Resolved] Sum Identity

    I have a project problem that reads:

    Show how to derive the sin(2x) from the sum identity using sin(x + x).
    Sounds easy. But I can't find anything about the sum identity in my book. Can anyone enlighten me?
    Last edited by The Hobo; Nov 26th, 2002 at 10:54 PM.
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  2. Nov 26th, 2002, 10:11 PM #2
    The Hobo
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    Okay. I fooled around with this:

    sin(x + x) = sin(x)cos(x) + cos(x)sin(x) = 2sin(x)cos(x)
    Where do I go from there? Am I going the wrong way?
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  3. Nov 26th, 2002, 10:26 PM #3
    rjlohan
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    Christ it's been awhile since I did these ones...
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  4. Nov 26th, 2002, 10:27 PM #4
    rjlohan
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    Do you have all the rules anywhere?
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  6. Nov 26th, 2002, 10:32 PM #5
    The Hobo
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    Originally posted by rjlohan
    Do you have all the rules anywhere?
    The rules? *scans his book* No one told me about rules?

    I have a crap-load of formulas I keep trying, but I'm not getting anywhere.

    I don't want an answer here. Just a clue to get me from A to B.
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  7. Nov 26th, 2002, 10:38 PM #6
    rjlohan
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    The clue is that you need the basic identities first.

    e.g - sin(x + y) = sin(x)cos(y) + sin(y)cos(x)

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  8. Nov 26th, 2002, 10:43 PM #7
    The Hobo
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    Bah! I got that.

    I'm here: 2sin(x)cos(x)

    How can I make that eqal to sin(2x)?

    When you substitute x for 45, they come out as equal, but that's too big of a jump. How can I prove those two are equal without pluging in a value?

    Is there some identity I'm not seeing?
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  9. Nov 26th, 2002, 10:49 PM #8
    The Hobo
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    fook me!

    The Double-Angle Formula states that:

    sin(2x) = 2sin(x)cos(x)
    I already have it solved.

    I can't believe I just wasted an hour on that when it's already a pre-established identity.

    Thanks for your help, rj.
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  11. Nov 28th, 2002, 04:53 PM #9
    SilverSprite
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    An hour?!?! Why would it take an hour? You should already know that sin(x+y)=sinxcosy+cosxsiny, and if you didnt you could refer to your book. Then it takes two seconds after that to say sin(x + x) = sin(x)cos(x) + cos(x)sin(x) = 2sin(x)cos(x)= sin(2x)
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  12. Nov 28th, 2002, 05:23 PM #10
    The Hobo
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    Originally posted by SilverSprite
    An hour?!?! Why would it take an hour? You should already know that sin(x+y)=sinxcosy+cosxsiny, and if you didnt you could refer to your book. Then it takes two seconds after that to say sin(x + x) = sin(x)cos(x) + cos(x)sin(x) = 2sin(x)cos(x)= sin(2x)
    Why should I already know that? Because you do? And I already mentioned that I didn't see it in the book.

    Way to be an ass, though.
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  13. Nov 28th, 2002, 06:01 PM #11
    bugzpodder
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    SilverSprite screwed up on a math contest so he isn't in a very good mood. Let me apologize for him.
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  14. Nov 28th, 2002, 07:41 PM #12
    SilverSprite
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    Yes, i guess i should apologize too. I CANT BELIEVE 9+5=11!!!! And what's even more stupid is a misadded so many times.
    YL says:"Few are those who see with their own eyes and feel with their own hearts."(Einstein)
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  15. Nov 29th, 2002, 04:38 PM #13
    Kalkewl8ter
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    He's not the only one who screwed up...
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  16. Nov 29th, 2002, 04:42 PM #14
    SilverSprite
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    Kalk how can you make such an amateur mistake!
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  17. Nov 29th, 2002, 05:20 PM #15
    bugzpodder
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    try (6a)/(3a)=3! (not 3 factorial, just 3 with an exclaimation mark)
    Massey RuleZ! ^-^__Cheers!__^-^ Massey RuleZ!


    Did you know that...
    The probability that a random rational number has an even denominator is 1/3 (Salamin and Gosper 1972)? This result is independently verified by me (2002)!
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