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Math Help - Trig equation

  1. #1
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    Trig equation

    2cos(3t-30deg)=-(square root of 2)
    [0,360)
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  2. #2
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    Hello,

    If t \in [0,360] then 3t \in [0,1080].

    Hence 3t-30=X \in [-30,1050].

    The problem is equivalent to finding X such as 2 \cos(X)=-\sqrt{2}

    \cos(X)=-\frac{\sqrt{2}}{2}

    We know that if \cos(X)=\cos(a) then the solutions are \left\{X=a+360k; X=-a+360k \ / \ k \in \mathbb{Z} \right\}

    We know that \cos(315)=\frac{-\sqrt{2}}{2}

    So find all solutions in [-30,1050] according to what i've written just before

    Then replace for t in X
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  3. #3
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    {\sqrt{2}}{2}
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