How do you graph #cos^2 x# and #sin^2 x#?
Of course, without some graphic tool, you can't make an exact graph, so I'll tell you the ideas which allow you, knowing the graphs of
- First of all, a square is always non-negative, so the graph will never go below the
- Since both sine and cosine functions are bounded in
#[-1,1]#, their squares will be bounded in #[0,1]#; in fact...
- When the function is negative, it becomes positive, because you're squaring it;
- When the function is zero, its square will still be zero;
- When the function is between zero and one, its square will be between zero and one, too;
- When the function equals one, its square will equal one, too.
So, if you start from the graph of
This is everything you can calculate perfectly. Once you have these break points, you must connect them with a line that resembles the one of