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Math Help - solving trigonometric equations with 2 variables

  1. #1
    zxe
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    solving trigonometric equations with 2 variables

    I finalized the question into 2 equations:

    -xcos70+ycos50-5.4=0...a
    xsin70+ysin50-23.9=0...b

    Just wondering, for a highschool grade 6th student or a first year university student, what is the fastest way to solve for x and y?

    I used matrix but it does not seem to be ideal, please see attachment.
    Attached Thumbnails Attached Thumbnails solving trigonometric equations with 2 variables-img_20110818_113211.jpg  
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  2. #2
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    Re: solving trigonometric equations with 2 variables

    Quote Originally Posted by zxe View Post
    I finalized the question into 2 equations:

    -xcos70+ycos50-5.4=0...a
    xsin70+ysin50-23.9=0...b

    Just wondering, for a high school grade 6th student or a first year university student, what is the fastest way to solve for x and y?

    I used matrix but it does not seem to be ideal, please see attachment.
    Multiply equation (a) by sin(70) and equation (b) by cos(70), then add the two equations and solve for y.
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  3. #3
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    Re: solving trigonometric equations with 2 variables

    Quote Originally Posted by zxe View Post
    I finalized the question into 2 equations:

    -xcos70+ycos50-5.4=0...a
    xsin70+ysin50-23.9=0...b

    Just wondering, for a highschool grade 6th student or a first year university student, what is the fastest way to solve for x and y?

    I used matrix but it does not seem to be ideal, please see attachment.
    Matrices should work ok...

    \displaystyle \begin{align*} \left[\begin{matrix}-\cos{70^{\circ}} & \cos{50^{\circ}} \\ \phantom{-}\sin{70^{\circ}} & \sin{50^{\circ}}\end{matrix}\right]\left[\begin{matrix}x \\ y\end{matrix}\right] &= \left[\begin{matrix}5.4 \\ 23.9\end{matrix}\right] \\ \left[\begin{matrix}x \\ y\end{matrix}\right] &= \left[\begin{matrix}-\cos{70^{\circ}} & \cos{50^{\circ}} \\ \phantom{-}\sin{70^{\circ}} & \sin{50^{\circ}}\end{matrix}\right]^{-1}\left[\begin{matrix}5.4 \\ 23.9\end{matrix}\right] \end{align*}
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