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suppose sin(x)=4/5 and cos(y)=-12/13, and x and y are in the second quadrant. determine the value of each expression: sin(x+y), cos(x-y), cos2x, sin2y.

  • trig -

    you should recognize the 3,4,5 and the 5,12, 13 right-angled triangles, so

    if sinx = 4/5, then cosx = -3/5 in II
    if cosy = -1213, then siny = 5/13 in II

    to have this type of question, you must also have come across the expansions for sin(A+B), cos(A-B), etc.

    I will do cos(x-y)

    cos(x-y) = cosx cosy + sinx siny
    = (-3/5)(-12/13) + (4/5)(5/13)
    = 56/65

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