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Math Help - Elimination

  1. #1
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    Exclamation Elimination

    Hey Guys,
    I am not sure how would you go about doing question 14? Anyone got any ideas?

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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: Elimination

    Strangely worded, but I think they want you to express y as a function of x. For example in the first one if you use the identity  \sin \theta = \sqrt {1- \cos^2 \theta} you can get an expression for y(x) which has no  \theta term in it.
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  3. #3
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    Re: Elimination

    That seems like a possible way. However, the answer is:
    x square/a square + y square/bsquare = 1
    Could you solve these trig equations simultaneously possibly?How would that work?
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  4. #4
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    Re: Elimination

    Trigonometric identities needed for these 2 questions:
    (a) cos^2(theta) + sin^2(theta) = 1. With that in mind, cos(theta) = x/a and sin(theta) = y/b. That's how you have (x/a)^2+(y/b)^2 = 1

    (a) tan^2(theta) + 1 = sec^2(theta). With that in mind, tan(theta) = x/a and sec(theta) = y/b. Then you have (x/a)^2 + 1 = (y/b)^2.

    Good day.
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  5. #5
    MHF Contributor ebaines's Avatar
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    Re: Elimination

    Did you try the approach I suggested? It gets to the same answer:

     y = b \sin \theta

    y = b \sqrt {1- \cos^2 \theta}

     y^2 = b^2(1- \cos^2 \theta)

     y^2 = b^2(1 - (\frac x a)^2)

     \frac {y^2}{b^2} + \frac {x^2}{a^2} = 1
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  6. #6
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    Re: Elimination

    Thanks ebaines and dennydengler
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