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Math Help - trouble reading sin graph, not accurate anymore?

  1. #1
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    trouble reading sin graph, not accurate anymore?

    my problem is that though I am aware i can use Rsin(x-a) to express this equation i never get the same answers as the book which uses Rcos(x+a). The book chose to express the equation as Rcos(x+a), however i want to express it as Rsin(x-a) because i am unable to read off the sin graph, it does not work anymore the reading are inaccurate. Can someone represent the equation as Rsin(x-a) and tell me how they got there?

    the books R(cos.. working
    the equation 7cos(x)-24sin(x)=Rcos(x+a)

    R=sqrt(7^2+24^2)=25

    cos a=(7/25)or sin a=(24/25) this results in a=73.74

    7cos(x)-24sin(x)=10

    25cos(x+73.74)=10

    cos(x+73.74)=0.4

    x+73.74=66.42, 360+/-66.42

    x=219.84, 352.68
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  2. #2
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    If you use Rsin(x-a) = R(sina*cosx - cosa*sinx)
    then tan(a) = sin(a)/cos(a)
    Find the value of a.
    Substitute in the equation and find the value of x.
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