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If sin x = -1/3 is in the 3rd quadrant and cos y = 2/5 is in the 4th quadrant, find the value of sec (x-y)

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3 answers

  1. cos(x-y) = cosx cosy + sinx siny = (-√8/3)(2/5) + (-1/3)(-√21/5)

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  2. sin x = -1/3 is in the 3rd quadrant
    then x = -1, r = 3 and
    x^2 + y^2 = r^2
    1 + y^2 = 9
    y = √8 = -2√2
    so we have cosx = -1/3, and sinx = -2√2/3

    cos y = 2/5 is in the 4th quadrant
    2^2 + y^2 = 25
    y = -√21
    so we have cosy = 2/5, and siny = -√21/5

    cos(x-y) = cosxcosy + sinxsiny
    = ... , you have those values, plug them in, then

    sec(x-y) = 1/cos(x-y) , flip your fraction

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  3. Error!

    In the first section , I interchanged sinx and cosx

    go with ooblecks's numbers

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