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Math Help - parametric equation

  1. #1
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    Talking parametric equation

    Hey all, sorry if this is in the wrong section. I'm in a precalc class but we're jumping between trig and this so not really sure anymore. Any help would be appreciated!

    a. Eliminate parameter t to find the equation in rectangular form.
    Sketch the curve defined by:
    <br />
x = \sec t,<br />
y = \tan^2 t,<br />
0\leq t \leq \pi<br />


    So far I made a chart with 3 columns, labeled: t, x, and y. For the t column I chose the values:
    <br />
\frac {\pi}{3},<br />
\frac {\pi}{4},<br />
\frac {\pi}{6},<br />
\frac {3\pi}{4},<br />
\frac {2\pi}{3},<br />
\frac {5\pi}{6}<br />

    Am I supposed to convert? If so, how do I convert  tan^2     t?
    <br />
\sec t = \frac {1}{\cos t}?<br />
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  2. #2
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    Quote Originally Posted by kevin11 View Post
    Hey all, sorry if this is in the wrong section. I'm in a precalc class but we're jumping between trig and this so not really sure anymore. Any help would be appreciated!

    a. Eliminate parameter t to find the equation in rectangular form.
    Sketch the curve defined by:
    <br />
x = \sec t,<br />
y = \tan^2 t,<br />
0\leq t \leq \pi<br />


    So far I made a chart with 3 columns, labeled: t, x, and y. For the t column I chose the values:
    <br />
\frac {\pi}{3},<br />
\frac {\pi}{4},<br />
\frac {\pi}{6},<br />
\frac {3\pi}{4},<br />
\frac {2\pi}{3},<br />
\frac {5\pi}{6}<br />

    Am I supposed to convert? If so, how do I convert  tan^2     t?
    <br />
\sec t = \frac {1}{\cos t}?<br />
    \tan^2{t} = \sec^2{t} - 1

    y = x^2 - 1
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  3. #3
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    Lexington, MA (USA)
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    Hello, kevin11!

    (a) Eliminate parameter t to find the equation in rectangular form.

    (b) Sketch the curve defined by: . \begin{Bmatrix}x &=& \sec t \\ y &=& \tan^2\!t\end{Bmatrix}\quad 0\leq t \leq \pi
    skeeter is absolutely correct!

    The equation is: . y \:=\:x^2-1\quad\hdots a parabola.
    . . It opens upward, vertex (0,-1), x-intercepts (1, 0)
    But there's more . . .


    I too made a chart and got these values (some approximate).

    . . \begin{array}{c|cc}<br />
t & x & y \\ \hline \\[-4mm]<br />
0 & 1 & 0 \\ \\[-4mm]<br />
\frac{\pi}{6} & 1.15 & 0.33 \\ \\[-4mm]<br />
\frac{\pi}{4} & 1.41 & 1 \\ \\[-4mm]<br />
\frac{\pi}{3} & 2 & 3 \end{array}
    L . \begin{array}{c|cc}<br />
\frac{\pi}{2} & \infty & \infty \\ \\[-4mm]<br />
\frac{2\pi}{3} & \text{-}2 & 3 \\ \\[-4mm]<br />
\frac{3\pi}{4} & \text{-}1.41 & 1 \\ \\[-4mm]<br />
\frac{5\pi}{6} & \text{-}1.15 & 0.33 \\ \\[-4mm]<br />
\pi & \text{-}1 & 0 \end{array}


    So the graph looks like this:


    Code:
                      |
          *          3+           *
                      |
           *          |          *
             *        |        *
        - - - - * - - + - - * - - - -
         -2    -1     |     1     2
                      |
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  4. #4
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    Hey guys, thanks for your help, really helped me out!
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