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Math Help - Differentiation of transcendental functions?

  1. #1
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    Differentiation of transcendental functions?

    ABCD is a trapezium with AB = CD, with vertices on the circle and with centre O. AD is a diameter of the circle. The radius of the circle is 4 units.

    a. Find BC in term of theta.
    b. Find the area of the trapezium in terms of theta and hence find the maximum area.


    Image of the diagram for this question:
    http://i45.tinypic.com/23s944h.png
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  2. #2
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    Re: Differentiation of transcendental functions?

    Quote Originally Posted by tutto00 View Post
    ABCD is a trapezium with AB = CD, with vertices on the circle and with centre O. AD is a diameter of the circle. The radius of the circle is 4 units.

    a. Find BC in term of theta.
    b. Find the area of the trapezium in terms of theta and hence find the maximum area.


    Image of the diagram for this question:
    http://i45.tinypic.com/23s944h.png
    1. The area of a trapezium is calculated by: area = \frac{top + base}2 \cdot height

    2. Replace:
    base = 2r
    height = r \cdot \sin(\theta)
    top = 2 r \cdot \cos(\theta)

    3. The area a is a function of \theta while r is a constant:

    a(\theta) = r^2 \sin(\theta) (1+\cos(\theta))

    4. Differentiate wrt \theta and solve a'(\theta) = 0 for \theta
    Attached Thumbnails Attached Thumbnails Differentiation of transcendental functions?-trapez_flaeche.png  
    Last edited by earboth; June 5th 2012 at 04:58 AM.
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