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Math Help - Rectangle Inscribed in Semicircle...Part 1

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    Rectangle Inscribed in Semicircle...Part 1

    A rectangle is inscribed in a semicircle of radius 1.

    (a) Express the area A of the rectangle as a function of the angle theta.

    (b) Show that A = sin(2theta)
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by magentarita View Post
    A rectangle is inscribed in a semicircle of radius 1.

    (a) Express the area A of the rectangle as a function of the angle theta.

    (b) Show that A = sin(2theta)
    um, what angle is theta?

    in any case, i think it would be a good idea for you do draw this on a pair of axis. let the rectangle sit on the x-axis with its top vertices touching the upper-half circle of radius 1 centered at the origin. try to center the rectangle also. see if that gives you any ideas
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    Hello, magentarita!

    A rectangle is inscribed in a semicircle of radius 1.

    (a) Express the area A of the rectangle as a function of \theta.

    (b) Show that: . A \:=\: \sin(2\theta)
    Code:
                  * * *
              *     |     *
            *-------+-------*
           *|       |     * |*
            |       |  1*   |y
          * |       | * θ   | *
          *-+-------+-------+-*
                        x

    The area of the rectangle is: . A \:=\:2xy

    We have: . x \:=\:\cos\theta,\;y\:=\:\sin\theta

    Therefore: . A \;=\;2\sin\theta\cos\theta \;=\;\sin2\theta

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  4. #4
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    Quote Originally Posted by Soroban View Post
    Hello, magentarita!

    Code:
                  * * *
              *     |     *
            *-------+-------*
           *|       |     * |*
            |       |  1*   |y
          * |       | * θ   | *
          *-+-------+-------+-*
                        x
    The area of the rectangle is: . A \:=\:2xy

    We have: . x \:=\:\cos\theta,\;y\:=\:\sin\theta

    Therefore: . A \;=\;2\sin\theta\cos\theta \;=\;\sin2\theta
    Good job Soroban. Nice try Jhevon.
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