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Math Help - Solving Trig Equations

  1. #1
    Junior Member
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    Solving Trig Equations

    I'm about done all my homework for this unit, but I seem to be stuck on my last 2 questions....any help would really be appreciated.

    Solve each equation:
    a) 2cos^2x + 3cosx -2 = 0

    and
    b) sinx = cos2x

    My lesson book is not very good on explaining the process of solving for x and provided very few examples....which is why I'm stuck. I just want to hand in my homework tonight and worry about understanding it when I can actually ask the teacher for help (which won't be until Monday)

    Thank you for any help you can give me!
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  2. #2
    Member arpitagarwal82's Avatar
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    1) Factorize the LHS of equation

    (2\cos x - 1) ( \cos x + 2) = 0
    => 2\cos x - 1 = 0 or   \cos x + 2 = 0
    => 2\cos x = 1 or \cos x = -2

    but \cos x cannot be -2.
    so  2\cos x = 1
    or \cos x = 1/2

    or x = 60 degree Answer

    b) \sin x = \cos 2x
    =>  sinx = 1 - 2\sin^2 x

    Proceed in above method. Factorize and calculate.
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  3. #3
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    does the answer end up being
    sinx = -1 and sinx = 1/2?
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  4. #4
    Member arpitagarwal82's Avatar
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    Quote Originally Posted by lil_cookie View Post
    does the answer end up being
    sinx = -1 and sinx = 1/2?
    Yes
    So x = -90 degree or x = 30 degree.

    Cheers.
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  5. #5
    Senior Member pankaj's Avatar
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    Better to write the answer in general form so as to include all possible solutions
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  6. #6
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    Got it, Thank you all!
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