Sin SquaredEdit
The graph of , or as it is more usually written, is shown below:
This function
 Must be nonnegative, 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
What about values that have on this graph? What values of will work? 
Amplitude, Frequency and Phase
Going from to

Cos SquaredEdit
The graph below does the same thing for
Once again, this function:
 Must be nonnegative, since the square of a negative number is always positive.
 Cannot exceed 1 since always lies between 1 and 1.
Comparing the two graphs it looks like they would sum to one. They do. This is a graphical way to see what we have already seen earlier, that:
Formula for cos squared
Using the fact that we have established that: and assuming the result we will prove later that: work out an expression for: Be careful with the signs and brackets as you are taking the minus of a minus. Be sure to simplify the formula  your answer should be at least as simple as the formula for . Does the formula you come up with look like it is consistent with the graph we have drawn for ? 