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Math Help - Finding Values for Quadratic Trigonometric Equation?

  1. #1
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    Finding Values for Quadratic Trigonometric Equation?

    The quadratic trigonometric equation a cos2 x + b cos x - 1 = 0 has the solutions (π/3), (π), and (5π/3) in the interval 0 < x < 2π. What are the values of a and b?

    I don't even know where to necessarily start with this question. Should I sub a certain value in for x? I tried that without any success.

    The answers are a = 2 and b = 1. Any suggestions would be very helpful, thanks in advance!
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  2. #2
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    Re: Finding Values for Quadratic Trigonometric Equation?

    Quote Originally Posted by misiaizeska View Post
    The quadratic trigonometric equation a cos2 x + b cos x - 1 = 0 has the solutions (π/3), (π), and (5π/3) in the interval 0 < x < 2π. What are the values of a and b?

    I don't even know where to necessarily start with this question. Should I sub a certain value in for x? I tried that without any success.

    The answers are a = 2 and b = 1. Any suggestions would be very helpful, thanks in advance!
    Set up a system of equations using the solutions (π/3), (π) and solve. Since x= (π/3), and x = (π) are solutions to the equations try plugging those values in.
    Thanks from misiaizeska
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  3. #3
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    Re: Finding Values for Quadratic Trigonometric Equation?

    Firstly the equation is a quadratic so it will have two solutions. The given solutions are π/3, π and 5π/3. We observe that π/3 and 5π/3 give the same value. So the solutions are π/3 and π. We know that cos π/3 = and cos π = -1.
    We can now form the equation having known the roots of the equation. The equation will be given by cos^2 x ( sum of the roots ) cos x + ( Product of the roots ) = 0. That gives
    Cos^2 x ( - 1 ) cos x + ( x -1 ) = 0
    On simplification we get,
    2cos^2 x + cos x 1=0
    Thus by comparison we have , a = 2 and b = 1
    Thanks from misiaizeska
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  4. #4
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    Re: Finding Values for Quadratic Trigonometric Equation?

    Thank you! ^_^
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  5. #5
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    Re: Finding Values for Quadratic Trigonometric Equation?

    Superb! Generally I never read whole articles but the way you wrote this information is simply amazing and this kept my interest in reading and I enjoyed it.
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