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Pre-Calculus

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How do you work this problem. I cannot find an example in the book to illustrate how to work it.

Find the value of tan(a-b) if cos a=-3/5, sin b=5/13, 90<a<180, and 90<b<180

Thanks for any help

  • Pre-Calculus -

    your text should have
    tan(a-b) = (tan a - tan b)/(1 + tanatanb)
    so you will need tan a and tan b

    cos a = -3/5 and a is in the second quadrant, so by sketching a diagram it is easy to see that sin a = 4/5 and
    tan a = - 4/3
    similarly sin b = 5/13 and b is in quadrant II, so cos b = -12/13 and
    tan b = -5/12
    then tan(a-b)
    =(-4/3 - (5/12))/(1 + (-4/3)(-5/12))
    = -33/56

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