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Math Help - Solving a system of trigonometric equations, for x and y (multivariable calculus).

  1. #1
    Mik
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    Solving a system of trigonometric equations, for x and y (multivariable calculus).

    Alright, here's the problem:

    theta = arctan(y/(x-1)) and phi = arctan(y/(x+1))

    I started off by taking the tangent of each side, which seemed obvious enough. So tan(theta) = y/x-1 and tan(phi) = y/x+1, but now I don't know of any method to isolate just the y and the x. Multiplying x-1 and x+1 to the other side doesn't help matters much, since it just adds an x to the other side that you still can't isolate.

    Anybody know how to go about solving this? Thanks.
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  2. #2
    Super Member ILikeSerena's Avatar
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    Re: Solving a system of trigonometric equations, for x and y (multivariable calculus)

    Quote Originally Posted by Mik View Post
    Alright, here's the problem:

    theta = arctan(y/(x-1)) and phi = arctan(y/(x+1))

    I started off by taking the tangent of each side, which seemed obvious enough. So tan(theta) = y/x-1 and tan(phi) = y/x+1, but now I don't know of any method to isolate just the y and the x. Multiplying x-1 and x+1 to the other side doesn't help matters much, since it just adds an x to the other side that you still can't isolate.

    Anybody know how to go about solving this? Thanks.
    Hi Mik!


    You have the equations:
    tan(theta) = y/(x-1) and tan(phi) = y/(x+1)

    (x-1)tan(theta) = y and (x+1)tan(phi) = y

    Equate the equations to each other:
    (x-1)tan(theta) = (x+1)tan(phi)

    Solve for x...
    Then calculate y from y=(x+1)tan(phi).
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