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Math Help - Area of a figure using trigonometry?

  1. #1
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    Area of a figure using trigonometry?

    The rotor blade of a helicopter is modelled using the following diagram, where TUVW is a square

    Code:
    (y-axis)
    |
    |  W      V
    |   _____
    |  /|    |
    |/  |____|      
    ---------------------------------- (x-axis)
    O    T    U
    
    theta is angle TOW.

    a) Show that the area of OTUVW is
    A = sin^2 ( theta ) + 1/4 sin ( 2 * theta )

    b) Express the are in the form k cos( 2 * theta - alpha ) + p

    c) Hence find the maximum are of the rotor blade, and the smallest positive value of theta when this maximum occurs

    Please help me solve part A, thats mainly what I need, I am pretty sure that I can do B & C. Yes, that is all the information given believe it or not. Sorry for the bad drawing, but point O is on the origin, and T and U are on the x-axis. Also, I couldn't get it in the drawing, but theta is angle TOW.
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  2. #2
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    Quote Originally Posted by kkroo View Post
    The rotor blade of a helicopter is modelled using the following diagram, where TUVW is a square

    Code:
    (y-axis)
    |
    |  W      V
    |   _____
    |  /|    |
    |/  |____|      
    ---------------------------------- (x-axis)
    O    T    U
    
    theta is angle TOW.
    a) Show that the area of OTUVW is
    A = sin^2 ( theta ) + 1/4 sin ( 2 * theta )

    this equation is only true if |OW| = 1
    ...
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