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Math Help - Trig Equations with Multiple Trig Functions help

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

    Find, to the nearest tenth of a degree, all values of x in the interval 0≤x≤360 that satisfy the equation.

    tan x=cos x

    also solve for x in the interval 0≤x≤2π


    cos x= cos x
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  2. #2
    o_O
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    \tan x = \cos x
    \tan x - \cos x = 0
    \frac{\sin x}{\cos x} - \cos x = 0
    \sin x - \cos^{2} x = 0 \quad \quad \mbox{Multiply both sides by } \cos x
    \sin x - \left(1 - \sin^{2} x\right) = 0
    \sin^{2} x + \sin x - 1 = 0

    Solve the quadratic for sin x and solve for x.

    -----------------

    \cos \left(\frac{1}{2}x\right) = \cos x
    \cos^{2}\left(\frac{1}{2}x\right) = \cos^{2} x
    \frac{1}{2} \left(1 + \cos x\right) = \cos^{2} x \quad \quad \mbox{Half-angle Identity}
    0 = \cos^{2} x - \frac{1}{2} \cos x - \frac{1}{2}
    0 = 2 \cos^{2} x - \cos x - 1

    You know the dril.
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