[quote]other student learning difficulty and suggestion for applet ?
the other part is the area under the curve "A*sin(w*t)" to ("A*sin(w*t)")^2 is half of the rectangle form by A*A and the period T. student cannot visualize this i feel.[/quote]

$A^2\sin^2\omega t + A^2\cos^2\omega t=A^2$
Let's calculate the average on both side.
The average of $A^2\sin^2\omega t$ should be the same as average of $A^2\cos^2\omega t$
And the sum of the above two average is $A^2$
So the average of $A^2\sin^2\omega t$ equal to $\frac{A^2}{2}$