I will do my best to describe the problem I am working on. The problem is not from a textbook or anything but something I am working on independently to strengthen my first year calculus knowledge. What I did is I took sin(x) and -sin(x) and graphed them together. Sin(x) and -sin(x) intersect at 0 and pi/2. These intersections will create a shape that resembles a ellipse and that is what i'm working with. What I did is I calculated the area of that shape. To do this I just found the area under the curve for sin(x) between 0 and pi/2 and added the absolute value of the area under the curve for -sin(x) from 0 to pi/2. I wanted to see how the area would increase as I increased/decreased the amplitude and period of the functions. I did this and found a very simple equation that is the same for increasing/decreasing amplitude and period. If I increase/decrease the period or amplitude of both functions equally, such as making the amplitude of both functions 3 or increasing period to 2pi I found an equation for the nth area, where n is any integer. An=4n. So if the amplitude of the function is 5, that is my n. I then did tangent and the same equation arises. So my question is, would this be expected? I was also surprised that the numbers would be so simple. Just a little collaboration on the problem would be appreciated. I'm looking for relations and things like that involving areas of trigonometric functions and put these relations into their most general form. Thanks.