Express A and B of equation y=Acos(wt) + Bsin(wt) in terms of R and d of equation Rcos(wt-d)?

Express A and B of equation y=Acos(wt) + Bsin(wt) in terms of R and d of equation Rcos(wt-d)?

I expanded Rcos(wt-d) and I got

R(cos(wt)cos(d) +sin(wt)sin(d)). Know I have no idea how to go on from here. This is a calculus type question

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  • GRAHAM
    Lv 6
    8 years ago
    Favorite Answer

    From your expansion you can observe:

    A=Rcos(d)

    B=Rsin(d)

    - that is it, although I think you were supposed to perform it the other way round, i.e. starting from the LHS.

    A final point is notice that A^2+B^2=R^2((sin^2(d)+cos^2(d))=R^2

    R=sqrt(A^2+B^2)

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