Math problem ...

Discussion in 'General Off-Topic Chat' started by MaHe, Nov 25, 2007.

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  1. MaHe
    OP

    MaHe one lazy schmo

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    tanx = - sqrt(15)
    90 degrees < x < 180 degrees

    Calculate sinx and cosx, using the calculator is forbidden. I actually know the results (sinx = sqrt(15)/4 and cosx = -1/4), but desperately need the procedure. Please help, if you can. [​IMG]
     
    #1 Nov 25, 2007
  2. castillo

    castillo Member

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    tanx = sinx/cosx ===> sinx = -sqrt(15)*cosx
    cosx^2 + sinx^2 = 1
    cosx^2 + (-sqrt(15)*cosx)^2 = 1
    cosx^2 + 15*cosx^2 = 1
    16*cosx^2 = 1
    cosx^2 = 1/16
    cosx = sqrt(1/16) = 1/4
    From this, you obtain sinx by "sinx^2 = 1 - cosx^2"

    Edit:
    As 90 < x < 180, cosx should be negative, so cosx = -1/4, not 1/4, sorry.
     
    #2 Nov 25, 2007
  3. Veho

    Veho The man who cried "Ni".

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    Oooh, can I try?

    tan(x) = -sqrt(15)

    square(tan(x)) = 15

    square(sin(x))/square(cos(x)) = 15;

    square(sin(x)) = 15square(cos(x))

    Since square(sin(x)) + square(cos(x)) = 1

    then: square(sin(x)) = 15(1-square(sin(x)))

    16square(sin(x)) = 15

    square(sin(x)) = 15/16

    Square(cos(x)) = (1 - 15/16)


    [​IMG]


    EDIT: Yeah, not done yet... oops [​IMG]

    Square(sin(x)) = 15/16 ==> sin(x) = +/- sqrt(15)/4

    square(cos(x)) = 1/16 ==> cos(x) = +/- 1/4


    If x is from the second quadrant (180>x>90),

    then sin(x) > 0,

    cos(x) < 0

    Meaning,

    sin(x) = sqrt(15)/4;

    cos(x) = -1/4.


    [​IMG]
     
    #3 Nov 25, 2007
  4. xcalibur

    xcalibur Gbatemp's Chocolate Bear

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    ugh... trigonometric identities...
    got a D because of these and integration
    redoing maths Alevel this year

    any tips? i tend to lose track of the whole process pretty quick
     
    #4 Nov 25, 2007
  5. wiithepeople

    wiithepeople ^^didn't play it that much, but I love it =D

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    the banned
    ...


    my brain hurts.
     
    #5 Nov 25, 2007
  6. MaHe
    OP

    MaHe one lazy schmo

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    Wow, thanks guys! The solution was right before my nose and I spent three hours. How the heck didn't I figure it out by myself? [​IMG]
    Anyways, I owe you both a beer or a dosen. [​IMG]
     
    #6 Nov 25, 2007
  7. xflash

    xflash Local Ninja

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    #7 Nov 25, 2007
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