The graph of , or as it is more usually written, is shown below:
Must be non-negative, since the square of a negative number is always positive.
Cannot exceed 1 since always lies between -1 and 1.
It looks like a sine or cosine wave shifted and compressed. It is. We will show this is true later when we look at double angle formulae and prove that .
Exercise: Spot check this
Is the graph correct? Try some actual avalues to see if they have been plotted in the correct place.
Any value where will be zero in this graph too.
Any value where will be 1 in this graph.
What about values that have on this graph? What values of will work?
Amplitude, Frequency and Phase
Going from to
The amplitude is halved. (the y values lie between 0 and +1, previously they were between -1 and +1).
The frequency is doubled. (we have more complete cycles in the same x distance.
The phase is... well we could argue that the phase is changed, but it really only makes sense to compare the phase of two waves of the same frequency, so it is hard to say what has happened to the phase.