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Math Help - Find Value of Trig. Expression

  1. #1
    Junior Member
    Joined
    Nov 2007
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    Find Value of Trig. Expression

    Hi,
    the directions are: find the exact value of the expression. Use a graphing utility to verify your results.

    I've done the problem but I'm not sure if I've done it right... and I'm also unsure about the negative in the original equation:

    the problem is::

    sec[arctan(-3/5)]

    this is what I've done so far-
    I drew the triangle using tan=opposite/adjacent

    Find Value of Trig. Expression-math.jpg

    then I used pythagorean theorem to find the hypotenuse. it was the square root of (34).

    after this I found the sec. which was the square root of (34)/5

    my question is if what I've is correct and where does the negative sign go in finding the solution?
    Am I supposed to just add it into the final answer???

    thank you!!

    p.s - I don't know how to make the square roots appear on the screen... that's why I wrote it out... everything in parentheses is under the square root.
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, overduex!

    Find the exact value of: . \sec\left[\arctan\left(-\frac{3}{5}\right)\right]

    You're thinking is correct . . . up to a point.


    Let \theta \,=\,\arctan\left(-\frac{3}{5}\right)\quad\Rightarrow\quad\tan\theta \:=\:-\frac{3}{5}

    Tangent is negative in Quadrants 2 and 4.


    There are two possible positions for angle \theta.
    Code:
                          |
              *           |
              :  *  √34   |
             3:     *     |
              :        *  |      5
          - - + - - - - - + - - - - - + - -
                   -5     |  *        :
                          |     *     :-3
                          |  √34   *  :
                          |           *
                          |

    Hence, there are two possible values for the secant.

    . . \sec\theta \;=\;\pm\frac{\sqrt{34}}{5}

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  3. #3
    Junior Member
    Joined
    Nov 2007
    Posts
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    Wow. Thanks!
    I had completely forgotten about the possibility of there being two positions for the angle.
    Thank you so much!!!
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