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Math Help - [SOLVED] equation with trigonometric and linear variable

  1. #1
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    [SOLVED] equation with trigonometric and linear variable

    I wasn't sure where to post this as i'm not sure if it's blindingly simple or more difficult, I'm an out of practice engineering student so either is just as likely
    anyway, just trying to solve for theta
    3 \theta - \sin \theta = 2 \pi

    I could easily get an answer using a calculator, but i want to do it analytically.
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  2. #2
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    Quote Originally Posted by dinNA89 View Post
    I wasn't sure where to post this as i'm not sure if it's blindingly simple or more difficult, I'm an out of practice engineering student so either is just as likely
    anyway, just trying to solve for theta
    3 \theta - \sin \theta = 2 \pi

    I could easily get an answer using a calculator, but i want to do it analytically.
    Not sure but this might help you
    Let f(\theta) = 3 \theta - \sin \theta - 2 \pi
    f'(\theta) = 3 - cos \theta >0
    So f(\theta) is increasing.

    f(0) = -2\pi < 0
    f(\pi) = \pi > 0
    so there is a root in [0,\pi]
    so on....
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  3. #3
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    is that just pretty much using guess and check? i was hoping for an exact answer.
    ---------------
    edit
    it seems that if i was to use that method i'd just use a calculator (not meaning to sound abrasive)
    Last edited by dinNA89; November 20th 2009 at 06:20 AM. Reason: more info
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  4. #4
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    Quote Originally Posted by dinNA89 View Post
    is that just pretty much using guess and check? i was hoping for an exact answer.
    ---------------
    edit
    it seems that if i was to use that method i'd just use a calculator (not meaning to sound abrasive)
    well...thts as much as i can help...
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  5. #5
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    i don't want you to feel unappreciated, i think it's admirable that you (and so many others) find time to help strangers with maths.
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  6. #6
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    Quote Originally Posted by dinNA89 View Post
    i don't want you to feel unappreciated, i think it's admirable that you (and so many others) find time to help strangers with maths.
    absolutely not...and reading threads here is my way to learn the subject...
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  7. #7
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    I believe Newton Method would have to be used or some other iterative method. It may be able to be solved analytically, but I kind of doubt it.
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  8. #8
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by dinNA89 View Post
    I wasn't sure where to post this as i'm not sure if it's blindingly simple or more difficult, I'm an out of practice engineering student so either is just as likely
    anyway, just trying to solve for theta
    3 \theta - \sin \theta = 2 \pi

    I could easily get an answer using a calculator, but i want to do it analytically.

    you can't find the exact value of it, you just can solve it numerically by bisection method or newtons method

    see this link for newton's method

    Newton's Method

    newton's method converges faster than bisection method so it is better

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  9. #9
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    Quote Originally Posted by Amer View Post
    you can't find the exact value of it, you just can solve it numerically by bisection method or newtons method

    see this link for newton's method

    Newton's Method

    newton's method converges faster than bisection method so it is better

    Newton's Method is more computationally expensive though, so I would not necessarily call it better. Secant method is another iteration method that can be used. Also, these methods will converge to different values based on an initial guess, because you are finding a root to a function that has more than one root. The root that you find will be dependent on the initial guess, so make sure you guess something near where you expect the solution to be based on your own requirements.
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  10. #10
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    yeah, i'm familiar with both of those methods and was hoping not to have to use them. Is there absolutely no way to get an exact solution?
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  11. #11
    Senior Member Shanks's Avatar
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    can you prove that its root is a rational or irrational number ?
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  12. #12
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    Quote Originally Posted by dinNA89 View Post
    yeah, i'm familiar with both of those methods and was hoping not to have to use them. Is there absolutely no way to get an exact solution?
    Probably not.
    If you could get something exact, then you would have a method of calculating \pi

     \pi = \dfrac{3 \theta - \sin \theta }{ 2}

    Seems to be an iteration problem
    .
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