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Math Help - Trig Problem

  1. #1
    Newbie
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    Apr 2009
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    Trig Problem

    The ‘London Eye’ can be considered to be a circular frame of radius 67.5m on the
    circumference of which are ‘capsules’ carrying a number of people round the circle. Take
    a co-ordinate system where O is the base of the circle and Oy is a diameter. At any time
    after starting off round the frame, the capsule will be at height h metres when it has
    rotated .°θ

    Apparently answer is... 67.5(1-Cosθ)??? why?

    Thanks
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  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
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    Hello, p4pri!

    Did you make a sketch?


    The ‘London Eye’ can be considered to be a circular frame of radius 67.5m
    on the circumference of which are ‘capsules’ carrying a number of people round the circle.
    Take a coordinate system where O is the base of the circle and OY is a diameter.
    At any time after starting off round the frame, the capsule will be at height h metres
    when it has rotated θ°.

    Apparently answer is: . 67.5(1-\cos\theta) . . . why?
    Code:
                  * * *
              *           *
            *               *
           *                 *
    
          *         C         *
      -   *         o         *
      :   *    R  * |         *
      :         * θ | Rcosθ
      R    *  *     |        *
      :   A o - - - + B     *
      :     : *     |     *
      -   --+-----*-*-*------
            D       O

    The center of the circle is C.
    The capsule is at A.
    \angle ACO = \theta

    The radius is: . CA =  CO = R

    In right triangle CBA\!:\;\cos\theta \:=\:\frac{CB}{R} \quad\Rightarrow\quad CB = R\cos\theta


    The height of the capsule is: . h \;=\;AD \;=\;BO \;=\;CO - CB \;=\;R - R\cos\theta

    Therefore: . h \;=\;R(1-\cos\theta)

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