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Math

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Angle x is in the second quadrant and angle y is in the first quadrant such that sinx=5/13 and cosy=3/5, determine and exact value for cos (x+y).
I have no idea how to even start this question. Could someone please help me?

  • Math -

    x=arcsin(5/13)
    y=arccos(3/5)

    so find those calculations and plug it into cos(x+y) or in other words
    cos(x+y)=(arcsin(5/13)+arccos(3/5))

  • Math - I still don't understand -

    Well, I understand what you mean by the solution, but I am getting a really long decimal as the answer, so that's not an excat value. Please, can you help me some more?

  • Math -

    Make diagrams of your triangles in the corresponding quadrants

    if sinx = 5/13 and is in II
    then cosx = -12/13

    if cosy = 3/5 and is in I
    then siny = 4/5

    cos(x+y) = cosxcosy - sinxsiny
    = (-12/13)(3/5) - (5/13)(4/5)
    = -56/65

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