I'll simplify this because of the formatting to 3 cycles using straight
lines. Assume starting at the "top" of a cycle. I have numbered the
"changes"

2 4
\ /\ /\ /
\ / \ / \ /
\/ \/ \/
1 3 5

At the first and last positions, there is not "change in direction".
Therefore the number of changes of direction = (cycle X 2) - 1

Only be starting mid-cycle do you get cycleX2

But I think we are going a little overboard on this.


Bert Byfield wrote:
Another great suggestion but probably will not help at my house.
My electricity can't make up it's mind. It changes directions
about 60 thousand times a second.

Make that 120.

If you guys are getting all technical, wouldn't it only *change*
direction 119 times?

Draw a graph of 60cps sine wave for 1 second. It will consist of 60
cycles in the form of full sine waves. Each peak, top and bottom, is a
change of direction. So: 120.