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Math Help - cosine of tangent

  1. #1
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    cosine of tangent

    The problem is to find Tan(B / 2)

    What is the cosine of Tan(B) when (pi/2 < B < pi) which would be quad 2.

    tanB = (sqrt(11) / 5)

    Seems to me that since tan = sine / cosine, the cosine would be 5, but Coursecompass.com (the site where I do all my homework) insists this is incorrect.

    TIA

    - Rusty
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  2. #2
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    Quote Originally Posted by estex198 View Post
    The problem is to find Tan(B / 2)

    What is the cosine of Tan(B) when (pi/2 < B < pi) which would be quad 2.

    tanB = (sqrt(11) / 5)

    Seems to me that since tan = sine / cosine, the cosine would be 5, but Coursecompass.com (the site where I do all my homework) insists this is incorrect.

    TIA

    - Rusty
    cosine of any angle must be between -1 and 1 ... it cannot equal 5.

    B is in quadrant II

    \tan{B} = \frac{-\sqrt{11}}{-5} = \frac{opposite \, side}{adjacent \, side}

    (-\sqrt{11})^2 + (-5)^2 = (hypotenuse)^2

    11 + 25 = 36

    hypotenuse = 6

    \cos{B} = \frac{adjacent \, side}{hypotenuse} = -\frac{5}{6}


    or, using an identity ...

    \tan{B} = \frac{\sqrt{11}}{5}<br />

    \sec^2{B} = 1 + \tan^2{B}

    \sec^2{B} = 1 + \frac{11}{25} = \frac{36}{25}

    \sec{B} = -\frac{6}{5}

    \cos{B} = -\frac{5}{6}
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  3. #3
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    Quote Originally Posted by skeeter View Post
    cosine of any angle must be between -1 and 1 ... it cannot equal 5.

    B is in quadrant II

    correction ... messed up my signs

    \tan{B} = -\frac{\sqrt{11}}{5}

    \tan{B} = \frac{\sqrt{11}}{-5} = \frac{opposite \, side}{adjacent \, side}

    (\sqrt{11})^2 + (-5)^2 = (hypotenuse)^2

    11 + 25 = 36

    hypotenuse = 6

    \cos{B} = \frac{adjacent \, side}{hypotenuse} = -\frac{5}{6}


    or, using an identity ...

    \tan{B} = -\frac{\sqrt{11}}{5}<br />

    \sec^2{B} = 1 + \tan^2{B}

    \sec^2{B} = 1 + \frac{11}{25} = \frac{36}{25}

    \sec{B} = -\frac{6}{5}

    \cos{B} = -\frac{5}{6}
    .
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  4. #4
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    thanks

    Skeeter, you rock man! Thanks for the help and for such a quick response. Peace.

    - Rusty
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