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Math Help - Finding Possible Values Of Trigonometric Expression

  1. #1
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    Angry Finding Possible Values Of Trigonometric Expression

    @MHF

    How is the answer to this trigonometric expression?

    \begin{array}{l}\cos x = \frac{1}{{11}}\\\frac{{\sec x - \tan x}}{{\sin x}} =  \pm \frac{{121\sqrt {30}  - 660}}{{60}}\end{array}

    Even when I start off I get the wrong answer for tangent x.

    \begin{array}{l}\tan x =  \pm \sqrt {{{\sec }^2}x - 1} \\\tan x =  \pm \sqrt {{{(11)}^2} - 1} \\\tan x =  \pm 20\sqrt 3 - 1 \end{array}

    Sam
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  2. #2
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    Re: Finding Possible Values Of Trigonometric Expression

    Quote Originally Posted by ArcherSam View Post
    @MHF

    How is the answer to this trigonometric expression?

    \begin{array}{l}\cos x = \frac{1}{{11}}\\\frac{{\sec x - \tan x}}{{\sin x}} =  \pm \frac{{121\sqrt {30}  - 660}}{{60}}\end{array}

    Even when I start off I get the wrong answer for tangent x.

    \begin{array}{l}\tan x =  \pm \sqrt {{{\sec }^2}x - 1} \\\tan x =  \pm \sqrt {{{(11)}^2} - 1} \\\tan x =  \pm 20\sqrt 3 - 1 \end{array}

    Sam
    I think you'll find that \displaystyle \begin{align*} \pm \sqrt{11^2 - 1} = \pm \sqrt{121 - 1} = \pm \sqrt{120} = \pm 2\sqrt{30} \end{align*}...
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  3. #3
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    Re: Finding Possible Values Of Trigonometric Expression

    @Prove It

    Lol, I should have checked if  \pm 20\sqrt 3 was equal to \sqrt {120} .

    With this I get:

    \begin{array}{l} \cos x = \frac{1}{{11}}\\ \sec x = \frac{1}{{\frac{1}{{11}}}} = 11\\ \tan x = \pm \sqrt {{{(11)}^2} - 1} = \sqrt {121 - 1} = \sqrt {120} = \pm 2\sqrt {30} \\ \sin x = \pm \sqrt {1 - {{(\frac{1}{{11}})}^2}} = \sqrt {1 - \frac{1}{{121}}} = \sqrt {\frac{{121}}{{121}} - \frac{1}{{121}}} = \sqrt {\frac{{120}}{{121}}} = \pm \frac{{2\sqrt {30} }}{{11}} \end{array}

    Then I am stuck!
    Last edited by ArcherSam; March 31st 2012 at 06:06 PM. Reason: Miscalculation
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  4. #4
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    Re: Finding Possible Values Of Trigonometric Expression

    So now you need to evaluate \displaystyle \begin{align*} \frac{\sec{x} - \tan{x}}{\sin{x}} \end{align*}...
    Thanks from ArcherSam
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  5. #5
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    Re: Finding Possible Values Of Trigonometric Expression

    @Prove It

    It was that easy!

    \begin{array}{l} \frac{{11 - ( + 2\sqrt {30} )}}{{ + \frac{{2\sqrt {30} }}{{11}}}}\\ 11(\frac{{11 - (2\sqrt {30} }}{{2\sqrt {30} }})\\ \sqrt {30} (\frac{{121 - 22\sqrt {30} }}{{2\sqrt {30} }})\\ \frac{{121\sqrt {30} - 22(30)}}{{60}}\\ \frac{{121\sqrt {30} - 660}}{{60}} \end{array}

    Thanks!
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