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Math Help - 【TRIGONOMETRY】help with one quiestion?

  1. #1
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    【TRIGONOMETRY】help with one quiestion?

    Question: If sin x + sin y =1 , what is the range of values of cos x + cos y?


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  2. #2
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    Re: 【TRIGONOMETRY】help with one quiestion?

    He HeilKing.

    Hint: Try using cos(x) = sin(x+pi/2) and simplifying.
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    Re: 【TRIGONOMETRY】help with one quiestion?

    Hey King
    This is a very tricky question . I am publishing a solution that is based on a lemma as discribed below.
    If anyone needs a proof of this lemma he has to sent me an e-mail.

    Attachment 28620
    Attached Thumbnails Attached Thumbnails 【TRIGONOMETRY】help with one quiestion?-panakis2.png  
    Last edited by MINOANMAN; June 15th 2013 at 03:19 AM.
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    Re: 【TRIGONOMETRY】help with one quiestion?

    Hi Heilking,
    I don't think Minoanman's answer is what you want. His inequality is not sharp. Here's what I think you want. Let the curve C have equation sin(x)+sin(y)=1. Then the set of values (range) {cos(x)+cos(y) : (x,y) is a point on C} = [-\sqrt3,\sqrt3]
    The first attachment shows the graph of C. From this graph (and analytically), you can see that the range can be found by considering only values of x and y in [0,pi].

    【TRIGONOMETRY】help with one quiestion?-mhftriga.png

    The second attachment shows the graph for C represented parametrically. From this representation, one can find the range. If you have any questions, just respond to this post.

    【TRIGONOMETRY】help with one quiestion?-mhftrig.png
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