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Math Help - Trig Equations with Multiple Trig Functions

  1. #1
    Member ~berserk's Avatar
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    Trig Equations with Multiple Trig Functions

    solve for Θ using the interval 0≤Θ≤360

    2cos^2 Θ+sinΘ=1

    The number of degrees in the smallest positive angle that satisfies the equation

    3cos2x+2 sin x+1=0
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  2. #2
    o_O
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    2\cos^{2} \theta + \sin \theta = 1
    2 \left(1 - \sin^{2} \theta \right)  + \sin \theta = 1
    2 - 2\sin^{2} \theta + \sin \theta = 1
    0 = 2\sin^{2} \theta - sin \theta - 1

    Factor and solve for \sin \theta and then \theta


    3\cos (2x) + 2 \sin x + 1 = 0
    3 \left( 1 - 2 \sin^{2} x \right) + 2 \sin x + 1 = 0 \quad \quad \mbox{Since: } \cos 2x = 1 - 2\sin^{2} x
    3 - 6 \sin^{2} x + 2\sin x + 1 = 0
    0 = 6\sin^{2} x - 2 \sin x - 4
    0 = 3\sin^{2} x - \sin x - 2

    Again factor and solve.
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