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Math Help - Solving a trig equation

  1. #1
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    Post Solving a trig equation

    Find, to the nearest degree, all values of theta in the interval 0 ≤ theta < 360
    that satisfy the equation 3 cos 2theta + sin theta 1 = 0.
    Last edited by mr fantastic; March 1st 2010 at 02:17 AM. Reason: Changed post title
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  2. #2
    Senior Member apcalculus's Avatar
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    At:

    Wolfram|Alpha

    enter the command:

    plot 3 cos(2x) + sin(2x) - 1 for x between 0 and 360 degrees

    it looks like the equation has four zeros in your interval. Use your graphing calculator to approximate them.

    Good luck!
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  3. #3
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    Hello, blame_canada100!

    Find, to the nearest degree, all values of \theta in the interval [0^o,\:360^o)

    that satisfy the equation: . 3\cos2\theta + \sin\theta  1 \:=\: 0
    Use the identity: . \cos2\theta \:=\:1-2\sin^2\!\theta


    The equation becomes: . 3(1-2\sin^2\!\theta) + \sin\theta - 1 \:=\:0 \quad\Rightarrow\quad 6\sin^2\!\theta - \sin\theta - 2 \:=\:0

    Factor: . (2\sin\theta + 1)(3\sin\theta - 2) \:=\:0


    And we have two equations to solve:

    . . 2\sin\theta + 1 \:=\:0 \quad\Rightarrow\quad \sin\theta\:=\:\text{-}\tfrac{1}{2} \quad\Rightarrow\quad \theta \:=\:210^o,\:330^o

    . . 3\sin\theta -2 \:=\:0 \quad\Rightarrow\quad \sin\theta \:=\:\tfrac{2}{3} \quad\Rightarrow\quad \theta \:\approx\:42^o,\:138^o

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