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Math Help - Solving sum and difference identities

  1. #1
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    Solving sum and difference identities

    Question:
    if  tanx=\frac{7}{3} and 0<x<\frac{\pi}{2} ;
     tany=0 and 0<x<\frac{\pi}{2}
    Find
    a)tan(x+y)
    b)tan(x-y)
    c) the quadrant containing (x-y)
    d)the quadrant containing (x+y)

    Attempt:

    Using the formula
     tan(x -/+ y) \frac{tanx +/- tany}{1 +/- tanx*tany}
    a)  \frac{7}{3}
    b) \frac{7}{3}
    c)1st quadrant
    d)1st quadrant

    Is my attempt Correct?



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  2. #2
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    Quote Originally Posted by mj.alawami View Post
    Question:
    if  tanx=\frac{7}{3} and 0<x<\frac{\pi}{2} ;
     tany=0 and 0<x<\frac{\pi}{2} ***

    tan(y) = 0 ?
    then y = 0, pi, or 2pi ... which one?


    Find
    a)tan(x+y)
    b)tan(x-y)
    c) the quadrant containing (x-y)
    d)the quadrant containing (x+y)

    Attempt:

    Using the formula
     tan(x -/+ y) \frac{tanx +/- tany}{1 +/- tanx*tany}

    formula correction ...

    \tan(x \pm y) = \frac{\tan{x} \pm \tan{y}}{1 \mp \tan{x} \cdot \tan{y}}
    .
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  3. #3
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    Quote Originally Posted by skeeter View Post
    .
    Ooh I am very sorry I misread the question properly

     tanx=\frac{7}{3} and it is in the first quadrant (0<x<[tex]\frac{\pi}{2});

     tany=\frac{3}{4} and it is in the first quadrant (0<y<[tex]\frac{\pi}{2})

    Find
    a) tan(x+y)
    b)tan (x-y)
    c) the quadrant containing (x-y)
    d)the quadrant containing (x+y)


    Attempt:
    a) \frac{19}{33}
    b) \frac{-37}{9}
    c)1st quadrant
    d)2nd quadrant/4th not sure
    Last edited by mj.alawami; February 28th 2009 at 11:17 AM.
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  4. #4
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    Quote Originally Posted by mj.alawami View Post
    Ooh I am very sorry I misread the question properly

     tanx=\frac{7}{3} and it is in the first quadrant (0<x<[tex]\frac{\pi}{2});

     tany=\frac{3}{4} and it is in the first quadrant (0<y<[tex]\frac{\pi}{2})

    Find
    a) tan(x+y)
    b)tan (x-y)
    c) the quadrant containing (x-y)
    d)the quadrant containing (x+y)


    Attempt:
    a) \frac{19}{33}
    b) \frac{-37}{9}
    c)1st quadrant
    d)2nd quadrant/4th not sure
    \tan(x+y) = -\frac{37}{9} ... quad II

    \tan(x-y) = \frac{19}{33} ... quad I
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