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Find cos(x + y) for cos x = -4/5 and sin y = 5/13 with x and y being in quadrant 2... HELP!!!?

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Find cos(x + y) for cos x = -4/5 and sin y = 5/13 with x and y being in quadrant 2... HELP!!!?

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  1. cos(x + y)

    = cos(x) cos(y) - sin(x) sin(y).

    In quadrant 2, sin(x) > 0:

    sin(x) = 3 / 5.

    In quadrant 2, cos(y) < 0:

    cos(y) = - 12 / 13.

    From (1):

    cos(x + y)

    = (- 4 / 5)(- 12 / 13) - (3 / 5)(5 / 13)

    = (48 - 15) / 65

    = 33 / 65.

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