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Math Help - Simplify for X? radian equation?

  1. #1
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    Question Arc Segments - Trig? Finding ratio (via golden angle)

    Attachment 20346
    This one has thrown me for a loop.
    Basically I have to simplify and then solve for x where y is 1 and c is (1+√5)/2
    and arc A = 2Pi(1 - 1/c)
    2(arc A) + 2(arc B) equal a full circle.
    I'm lost, any help is appreciated. Thank you.
    Attached Thumbnails Attached Thumbnails Simplify for X? radian equation?-simplifyforx.jpg  
    Last edited by DaveLevy; January 6th 2011 at 05:28 PM. Reason: Changing thread name...
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  2. #2
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    [Edit]

    Note that if R was the radius, Y = 2R\sin(B/2) and X = 2R\sin(A/2).

    So, X=Y\frac{\sin(A/2)}{\sin(B/2)}.

    I think you should be able to go from there.
    Last edited by snowtea; January 6th 2011 at 11:49 AM.
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  3. #3
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    Using that I got A=2.3999632297287 and X = .38880073356013 if Y=1 ... I know this is not correct because x>y ... could you maybe expound upon that further simplifying A and B into the equation so I can see what's supposed to happen? thank you, I really appreciate your help

    So basically I'm looking at it like this:
    X=Y(cos(A/2)/cos(B/2)), Y=1, B=(2Pi-2A)/2, A=2Pi(1-1/c), c=(1+Root of 5)/2

    Am I right about B at this first step?
    Last edited by DaveLevy; January 6th 2011 at 11:40 AM. Reason: Adding to
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  4. #4
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    Oops, it should have been sin and not cos.
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  5. #5
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    Okay... so in that case I got x ~ 2.57... is that correct?

    Edit:
    Could someone help show me the step by step on how to solve this properly if you have the time and kindness? thank you.
    Last edited by DaveLevy; January 6th 2011 at 02:35 PM. Reason: Not sure...
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  6. #6
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    I'm not that great adding drawings to posts, so I'll try to describe it.

    To get Y = 2R\sin(B/2), in the diagram, the rectangle is divided into 4 triangles. Look at one of these triangle with side length Y.
    Bisect the angle of the triangle from the center of the circle, and you have two right triangles.
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  7. #7
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    Arrow Trying to solve... ????

    Simplify for X? radian equation?-solveattempt1.jpg

    This is driving me nutty... okay so in that scenario the hypotenuse is the radius... however when I try to solve for X I get all wrong values... no matter which trig function I use... so what could I be doing incorrectly?
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