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Math Help - Revision Questions

  1. #1
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    Question Revision Questions

    Hey guys

    Could someone please explain to me how to do these questions? I can't seem to b able to figure them out. Thanx!
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  2. #2
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    Quote Originally Posted by xwrathbringerx View Post
    Hey guys

    Could someone please explain to me how to do these questions? I can't seem to b able to figure them out. Thanx!
    I'll try #3:

    "If a^2 + b^2 < c^2, show that
    a \cos \theta + b \sin \theta = c has no real roots."

    Let x = \sin \theta, so \cos \theta = \sqrt{1 - x^2}.

    Then the equation becomes
    a \sqrt{1 - x^2} + b x = c

    so

    a \sqrt{1 - x^2} = c - bx

    squaring both sides,

    a^2 (1 - x^2) = (c - bx)^2

    You now have a quadratic equation in x. Find the discriminant of the equation and I think you will see the solution.
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