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Math Help - sine inverse and theta value

  1. #1
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    sine inverse and theta value

    is it possible to find the value of x in sin x = \frac {\sqrt {5}-1}{4} without a calculator?

    another question..

    find the value of theta if cos(2 \theta)-sin(\theta)=\theta

    also ..

    find the length of the hypotenuse in a right triangle if the sum of its three sides is 200.
    Last edited by eq123; April 18th 2010 at 02:25 PM. Reason: adding another question
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  2. #2
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    Quote Originally Posted by eq123 View Post
    is it possible to find the value of x in sin x = \frac {\sqrt {5}-1}{4} without a calculator?

    another question..

    find the value of theta if cos(2 \theta)-sin(\theta)=\theta

    also ..

    find the length of the hypotenuse in a right triangle if the sum of its three sides is 200.
    Please provide some context for these (that is on what part of your course did they arise and what course for that matter).

    CB
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  3. #3
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    these problems are not related to the study of a specific course.. they are just some problems that i find interesting..
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by eq123 View Post
    these problems are not related to the study of a specific course.. they are just some problems that i find interesting..
    Then they are not trigonometry, and I will move them; I think to the Calculus forum.

    CB
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  5. #5
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    Quote Originally Posted by eq123 View Post
    is it possible to find the value of x in sin x = \frac {\sqrt {5}-1}{4} without a calculator?

    another question..

    find the value of theta if cos(2 \theta)-sin(\theta)=\theta

    also ..

    find the length of the hypotenuse in a right triangle if the sum of its three sides is 200.
    The first two you will need to find the roots numerically.


    CB
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    i don't think that these problems are related to calculus..

    anyway, can you provide any additional information?
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  7. #7
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    Quote Originally Posted by eq123 View Post
    i don't think that these problems are related to calculus..

    anyway, can you provide any additional information?
    Google for "numerical solution of non-linear equations", "Newton Raphson" and/or "bisection algorithm"

    CB
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  8. #8
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    i am still trying to figure out the solution for these problems .. especially for the question cos(2 \theta)-sin(\theta)=\theta .. i would appreciate it if anyone can provide a step by step solution..
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  9. #9
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    Quote Originally Posted by eq123 View Post
    i am still trying to figure out the solution for these problems .. especially for the question cos(2 \theta)-sin(\theta)=\theta .. i would appreciate it if anyone can provide a step by step solution..
    This almost certainly has a solution which cannot be expressed in closed form using elementary functions and well known constants.

    Sketch the curve y=\cos(2 \theta)-\sin(\theta)-\theta and it is obvious that it has a single root between 0 and 1. The using the Bisection or NR algorithms you will find that the root is \approx 0.372087

    CB
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  10. #10
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    thank you. i was able to find the solution using newton raphson method.
    Last edited by eq123; April 21st 2010 at 10:39 AM.
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