Trigonometry/Graph of Sine Squared
Sin Squared[edit  edit source]
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 Squared[edit  edit source]
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 ? 