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Math Help - trigo problem no. 23

  1. #1
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    trigo problem no. 23

    trigo problem no. 23
    p213 q14
    Thankstrigo problem no. 23-out0090.jpeg

    trigo problem no. 23-out0091.jpeg
    trigo problem no. 23-out0092.jpeg
    Last edited by afeasfaerw23231233; March 20th 2008 at 05:51 AM.
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  2. #2
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    I think the important word you are missing is "suitable". You should have THREE double-angle formulas for cosine.

    \cos(2\theta)\;=\;2\cos^{2}(\theta)-1\;=\;1-2\sin^{2}(\theta)\;=\;\cos^{2}(\theta)-\sin^{2}(\theta)

    I believe you will find the last most "suitable" for your conditions. It factors as a difference of squares and should be obvious from there.
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    that mean the 'hint ' from the book is useless! it directs me to the wrong way to do this question!
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    Quote Originally Posted by afeasfaerw23231233 View Post
    that mean the 'hint ' from the book is useless! it directs me to the wrong way to do this question!
    It is a quite useful hint. In fact, I think it's rather clever.
    cos(2\theta) = sin(\theta) + cos(\theta)

    Now use the hint: cos(2\theta) = cos^2(\theta) - sin^2(\theta)

    cos^2(\theta) - sin^2(\theta) = cos(\theta) + sin(\theta)

    Now factor the left hand side and see what comes of it.

    -Dan
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    Quote Originally Posted by topsquark View Post
    It is a quite useful hint. In fact, I think it's rather clever.
    cos(2\theta) = sin(\theta) + cos(\theta)

    Now use the hint: cos(2\theta) = cos^2(\theta) - sin^2(\theta)

    cos^2(\theta) - sin^2(\theta) = cos(\theta) + sin(\theta)

    Now factor the left hand side and see what comes of it.

    -Dan
    thank you for your help! why i thought of it for such a long time but couldn't see it. thanks again.
    EDIT: ah.. TKhunny already gave the hint to me but i was in a hurry and didn't see it. how stupid i am....
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by afeasfaerw23231233 View Post
    thank you for your help! why i thought of it for such a long time but couldn't see it. thanks again.
    EDIT: ah.. TKhunny already gave the hint to me but i was in a hurry and didn't see it. how stupid i am....
    Not stupid...you've just not had enough experience at it. This is how you get experience.

    -Dan
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    Let's put a couple of things on your list of things to learn:

    1) Have a little patience with yourself. No sense beating yourself up. Not everything is easy.

    2) Just a little LaTeX can go a long way. It takes up WAY less space than scanned images.

    Good deal. What else are you working on?
    Last edited by TKHunny; March 26th 2008 at 05:10 AM.
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