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    Hey TSR. Any guidance on how to do the following:

    - Write 12 cosx-5sinx in the form Rcos(x+Φ), giving Φ to 0.1o

    and

    - Hence solve 12 cosx-5sinx = 7.8 for -180o<x<180o


    Many thanks, people

    Yannis
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    (Original post by yannispress)
    Hey TSR. Any guidance on how to do the following:

    - Write 12 cosx-5sinx in the form Rcos(x+Φ), giving Φ to 0.1o

    and

    - Hence solve 12 cosx-5sinx = 7.8 for -180o<x<180o


    Many thanks, people

    Yannis
    Do you know how to express sums of trig functions in Harmonic form?
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    (Original post by yannispress)
    Hey TSR. Any guidance on how to do the following:

    - Write 12 cosx-5sinx in the form Rcos(x+Φ), giving Φ to 0.1o

    and

    - Hence solve 12 cosx-5sinx = 7.8 for -180o<x<180o


    Many thanks, people

    Yannis
    The first identity you will need - which you should find in your formula booklet - is cos(A + B) = cos(A)cos(B) - sin(A)sin(B).

    You will therefore have Rcos(x + \phi) = Rcos(\phi)cos(x) - Rsin(\phi)sin(x) and hence Rcos(\phi) = 12 and Rsin(\phi) = 5.

    To find R you can use the identity sin^2(x) + cos^2(x) = 1.

    To find \phi you can eliminate R using the two equations above. This is best done by simply dividing one equation by the other.

    For the last part, having eliminated the sin(x) term you can just solve normally by dividing both sides by R and using inverse cosine.
 
 
 
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