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Math Help - Simultaneous equations involving cos and sin

  1. #1
    Junior Member CuriosityCabinet's Avatar
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    Simultaneous equations involving cos and sin

    (cos \theta)x - (sin \theta)y=2
    (sin\theta)x + (cos \theta)y=1

    In the range 0 \leq \theta < 2 \pi is it solvable? Or are there values of theta when the equations are not solvable?
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  2. #2
    MHF Contributor

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    Quote Originally Posted by CuriosityCabinet View Post
    (cos \theta)x - (sin \theta)y=2
    (sin\theta)x + (cos \theta)y=1

    In the range 0 \leq \theta < 2 \pi is it solvable? Or are there values of theta when the equations are not solvable?
    Assuming you mean to solve for x and y, just treat sin(\theta) and cos(\theta) as constants. In particular, you can multiply the first equation by cos(\theta), the second equation by sin(\theta), and add the equations to eliminate y. A system of equations would be "non-solvable" if and only if the resulting coefficient of x were 0. But a rather nice thing happens here!
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