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Math Help - 2 very difficult trig problems

  1. #1
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    2 very difficult trig problems

    Having an extremely difficult time solving 2 problems. Have posted it as a photo attachment. The first 2 paragraphs & diagram relate to the 1st problem. The last paragraph is for the second problem.

    For the second problem, I tried using double-angle formula, but I don't know where to go after that. For the first problem, I am completely lost. Any help would be appreciated. Thanks
    Attached Thumbnails Attached Thumbnails 2 very difficult trig problems-trig.jpg  
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    Re: 2 very difficult trig problems

    I don't understand why changing the number of bearings changes anything. It just looks like it would fill up more of the space around the hub. If you could explain that I might be able to help.
    Thanks from topsquark
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    Re: 2 very difficult trig problems

    ...And in the future please put your problem so it's right side up!

    -Dan
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    Re: 2 very difficult trig problems

    I think the diagram is a little misleading. It's just meant to show you what a, b, and c are. When there are three bearings, they fill up the entire circle, touching each other (i.e. a will be very small and b very big). As you add more ball bearings, a increases and b decreases. I think that's what the problem is trying to say.
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    Re: 2 very difficult trig problems

    2 very difficult trig problems-balls.png

    The attached figure explains the first problem more clearly. Fig 1 to 4 depicts the configuration for 3,4,5,6 ball bearing cases receptively.

    As in Fig 5 lets consider the n-ball bearing case.

    \sin \theta = \frac{ID}{DL} = \frac{b}{a+b} \implies \frac{a}{b} = \csc \theta  - 1 where  \theta = \frac{\pi}{n} as it depicts a regular n-sided polygon.

    Other ratios are easy as we have c= a+2b

    Kalyan.
    Last edited by kalyanram; May 21st 2013 at 01:23 AM.
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    Member kalyanram's Avatar
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    Re: 2 very difficult trig problems

    HINT: For the second problem use the identity \sin (90 \pm x) = \mp \cos x and the identity sin^2 x + cos^2 x =1.

    Kalyan.
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    Re: 2 very difficult trig problems

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    Re: 2 very difficult trig problems

    2 very difficult trig problems-22-may-13-1.png
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    Re: 2 very difficult trig problems

    Quote Originally Posted by ibdutt View Post
    Click image for larger version. 

Name:	22 May 13 -1.png 
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    I have gone wrong and i am sorry. kalyanram is very correct and MINOANMAN has referred a good site.
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