Thread: 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.

Originally Posted by kkroo

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

...