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Math Help - [SOLVED] tangent sum identity issue

  1. #1
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    [SOLVED] tangent sum identity issue

    I've been working through a tanget sum identity problem and I've mostly got it, except I've got the signs reversed. I was curious if someone could point out the mistake I made. I apologize for how long this is. All assistance is appreciated.

    Problem is
    tan(A+B)
    where
    sinA = \frac{-3}{5}
    is in QIII
    and
    cosB = \frac{-1}{4}
    is in QII

    sinA= \frac{-3}{5} so the hypotenuse is 5, the oppose side is -3, making the adacent side 4. Thus tan(A) = \frac{-3}{4}.

    for B, cosB= \frac{-1}{4} so the hypotenuse is 4, the adjacent side -1, making the opposite side \sqrt15. Thus tan(b) = \frac{\sqrt15}{-1} or just -\sqrt15.

    The tangent sum identity is \frac{tanA+tanB}{1-tanAtanB}

    Substituting in, I get
    \frac{\frac{-3}{4}+ -\sqrt15}{1-\frac{-3}{4}(-\sqrt15)}

    which is
    \frac{\frac{-3-4\sqrt15}{4}}{1-\frac{3\sqrt15}{4}}
    and then
    \frac{\frac{-3-4\sqrt15}{4}}{\frac{4-3\sqrt15}{4}}
    followed by
    \frac{-3-4\sqrt15}{4}*\frac{4}{4-3\sqrt15}
    and finally
    \frac{-3-4\sqrt15}{4-3\sqrt15}

    unfortunately, the answer would appear to be
    \frac{3-4\sqrt15}{4+3\sqrt15}

    Can someone please point out my mistake?
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  2. #2
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    Quote Originally Posted by satis View Post
    I've been working through a tanget sum identity problem and I've mostly got it, except I've got the signs reversed. I was curious if someone could point out the mistake I made. I apologize for how long this is. All assistance is appreciated.

    Problem is
    tan(A+B)
    where
    sinA = \frac{-3}{5}
    is in QIII
    and
    cosB = \frac{-1}{4}
    is in QII

    sinA= \frac{-3}{5} so the hypotenuse is 5, the oppose side is -3, making the adacent side (negative) 4. Thus tan(A) = \textcolor{red}{\frac{-3}{-4}}.

    here is your mistake ... in quad III, tangent is positive



    Can someone please point out my mistake?
    ...
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  3. #3
    Junior Member
    Joined
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    awesome, thank you very much. I seem to be making that mistake a lot. I'm just happy my methodology is sound (other than screwing up signs).
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