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Math Help - Solve for Theta

  1. #1
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    Solve for Theta

    Its been a while since I really had to deal with an equation like this, and I might just be missing a simple trig identity. I would really appreciate any help you might be able to give me.

    I don't believe I have made any mistakes getting here because I can extrapolate the solution from a graphing calc, and the solution works in my application.

    I am trying to solve for Θ in the following equation (I am working in degrees):

    ΔL = (π * r * Θ / 45) - (4 * r * sinΘ)
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  2. #2
    Super Member bigwave's Avatar
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    Quote Originally Posted by gwammy View Post
    Its been a while since I really had to deal with an equation like this, and I might just be missing a simple trig identity. I would really appreciate any help you might be able to give me.

    I don't believe I have made any mistakes getting here because I can extrapolate the solution from a graphing calc, and the solution works in my application.

    I am trying to solve for Θ in the following equation (I am working in degrees):

    ΔL = (π * r * Θ / 45) - (4 * r * sinΘ)
    what does the "triangle L" mean

    otherwise is this the equation

     <br />
?? = \frac{\pi r \theta}{45^o} - 4 r \sin{\theta}<br />

    also, mixing degree's with \pi is confusing
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  3. #3
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    The Triangle is a "delta". It signifies a change in that value. In this case, I am working out the change in length of a series of arcs that starts and ends at the same points of a straight line.

    Yes, working with degrees when using PI can be confusing, and I could change it, but the CAD program that I am working with works best in degrees, not radians. I apologize for confusing the numbers further.

    All of that aside, your equation is correct.
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  4. #4
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    Simplified version

    Essentially, after simplifying further, I am just looking to solve for Θ for the following:

    X = Θ - sin Θ
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  5. #5
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    Hello gwammy
    Quote Originally Posted by gwammy View Post
    Essentially, after simplifying further, I am just looking to solve for Θ for the following:

    X = Θ - sin Θ
    You won't be able to get an exact solution to an equation like this. You'll have to use some sort of numerical method ; e.g. Newton's method. Or if you have access to a spreadsheet (e.g. Excel), then it's very quick to use a 'goal seek' method to find \theta to give a particular value of x.

    Grandad
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  6. #6
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    Thanks for your help! It works great in excel.
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