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Math Help - Sin Problem

  1. #1
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    Sin Problem

    Hello everyone,
    I'm having some trouble solving this equation.
    Sin Problem-2.36.jpg
    All help would be appreciated , Thanks!
    This is my work that I've done so far...
    Sin Problem-2012-05-09-22.24.39.jpg

    PS I know this might not be the right section for a statics problem, but I'm really only having trouble with the trig part so yeah... lol
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  2. #2
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    Re: Sin Problem

    When I plugged back in my 58.91 degrees, I should have gotten 0, but I get something like 82.8 not 0.
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  3. #3
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    Re: Sin Problem

    a)

    \begin{cases}90+70\cdot \sin \alpha-130 \cdot \cos \alpha=0 \\\sin^2 \alpha + \cos^2 \alpha=1 \end{cases}
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  4. #4
    Member srirahulan's Avatar
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    Re: Sin Problem

    how do you enter this cos alpha and other maths symbols in this text pad?
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  5. #5
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    Re: Sin Problem

    princeps, I tried that already (if you look in the picture of the work I showed), and when I solved for alpha I got 58.91 degrees. However, upon plugging it back into the problem I don't get 0.
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  6. #6
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    Re: Sin Problem

    starting where \sum F_y = 0 , 4th line ... one "egregious" algebra error.

    note (a-b)^2 \ne a^2 + b^2
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  7. #7
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    Re: Sin Problem

    Ahhhh I see. Thank you !
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  8. #8
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    Re: Sin Problem

    a\cos{x} - b\sin{x} = R\cos(x+t)

    R = \sqrt{a^2+b^2} , \tan{t} = \frac{b}{a}

    let x = your " \alpha" ...

    13\cos{x} - 7\sin{x} = 9

    R = \sqrt{13^2 + 7^2} , t = \arctan\left(\frac{7}{13}\right)

    R \cos(x + t) = 9

    x+t = \arccos\left(\frac{9}{R}\right)

    x = \arccos\left(\frac{9}{R}\right) - \arctan\left(\frac{7}{13}\right) \approx 24.14^\circ
    Thanks from detex
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