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Math Help - trig putting in for rcos(x-a)

  1. #1
    Member
    Joined
    Sep 2005
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    84

    trig putting in for rcos(x-a)

    Hello

    I need help with some this type of trig question

    can you someone please go throught the process of solving it so thats its in the form that is required. I am unsure on how to do these type of questions

    thanks
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  2. #2
    MHF Contributor
    Joined
    Nov 2008
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    France
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    1,458
    Hi

    a cos x + b sin x = \sqrt{a^2 + b^2} \:\left( \frac{a}{\sqrt{a^2 + b^2}} cos x + \frac{b}{\sqrt{a^2 + b^2}} sin x \right)

    \frac{a}{\sqrt{a^2 + b^2}} and \frac{b}{\sqrt{a^2 + b^2}} can be seen respectively as the cosines and the sinus of the same angle \theta because the sum of their square is equal to 1

    Therefore

    a cos x + b sin x = \sqrt{a^2 + b^2} \:\left( cos \theta cos x + sin \theta sin x \right) = \sqrt{a^2 + b^2} \:cos(x-\theta)
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