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Thread: Trig question

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    mj8
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    Trig question

    I'm having trouble with this question. Normally i would use auxiliary method but I'm having difficulty. Thanks in advance.

    (i) Express 2cosθ + 2cos(θ + π∕3) in the form Rcos (θ + α), where R > 0 and, 0 < α < π/2

    (ii) Hence, or otherwise, solve 2cosθ + 2cos(θ + π∕3) = 3, for 0 < α < 2π

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    617 pages fan96's Avatar
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    Re: Trig question

    Hint: use the identity



    And note that



    is a constant.
    Last edited by fan96; 31 Mar 2018 at 8:46 PM.

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    Senior Member integral95's Avatar
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    Re: Trig question

    Quote Originally Posted by mj8 View Post
    I'm having trouble with this question. Normally i would use auxiliary method but I'm having difficulty. Thanks in advance.

    (i) Express 2cosθ + 2cos(θ + π∕3) in the form Rcos (θ + α), where R > 0 and, 0 < α < π/2

    (ii) Hence, or otherwise, solve 2cosθ + 2cos(θ + π∕3) = 3, for 0 < α < 2π
    you have to expand the second term first using your sum of angles and simplify before you use your usual auxiliary angle.

    fan96 did suggest a faster method, though that formula isn't in the syllabus anymore.
    “Smart people learn from their mistakes. But the real sharp ones learn from the mistakes of others.”
    ― Brandon Mull

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    mj8
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    Re: Trig question

    Thanks!

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