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Math Help - Solving a trigonometric equation

  1. #1
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    Solving a trigonometric equation

    The problem:

    http://s13.postimage.org/8rlczwkyv/solve.png

    Hi. I was able to find the solution, option D, by plugging the different angles. I'm not sure if this is the best way to solve the problem though. Any ideas?
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  2. #2
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    Re: Solving a trigonometric equation

    Quote Originally Posted by Frederick View Post
    The problem:
    http://s13.postimage.org/8rlczwkyv/solve.png
    Hi. I was able to find the solution, option D, by plugging the different angles. I'm not sure if this is the best way to solve the problem though. Any ideas?
    You might note the it is equivalent to: 2\sec^2(x)-3\sec(x)-2=0.
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  3. #3
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    Re: Solving a trigonometric equation

    First, do you know the basic definitions and trig identities? The very first thing I recommend is writing every thing in terms of sine and cosine, using the definitions of "tangent" and "secant". Then use a trig identity to write a quadratic equation in terms or "cosine" only and, finally, solve the equation.

    I see Plato got in just ahead of me and suggested writing it as a quadratic equation in "secant" rather than "cosine"! Much of a muchness.
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  4. #4
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    Re: Solving a trigonometric equation

    I tried the quadratic formula way for a different problem but I didn't get the right solution:

    http://s14.postimage.org/z6kdxz5n5/problem.jpg

    is there a difference between writing it as a quadratic formula in sine or any of the other basic trig definitions?
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  5. #5
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    Re: Solving a trigonometric equation

    Quote Originally Posted by Frederick View Post
    I tried the quadratic formula way for a different problem but I didn't get the right solution:
    http://s14.postimage.org/z6kdxz5n5/problem.jpg
    is there a difference between writing it as a quadratic formula in sine or any of the other basic trig definitions?
    (2\sec(x)+1)(\sec(x)-2)=0 tells us that sec(x)=2 or x=\frac{\pi}{3}~\&~\frac{5\pi}{3}.
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  6. #6
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    Re: Solving a trigonometric equation

    I found out that the solution of the last problem I posted can be found by simply factoring. Changing to secant is unnecessary.
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  7. #7
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    Re: Solving a trigonometric equation

    Reply #5 addresses the first post. Besides I even read the attachment in your reply #4!
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