Question

Graph y=sin(x) and y=cos(x), and find the first two points of intersection after x=0. Then find the area bounded by the two between those two points.

Please help!

Answer 1

Hmm graphing it won't help us find the points of intersection too well. I think we'd rather approach it algebraically or by using the unit circle.

Doing it with algebra is a little more work, but if you're rusty on your unit circle, it might make more sense to you.

Answer 2

Try to recall that, on the unit circle, the sine function represents movement along the y-axis, while the cosine function represents movement along the x-axis.

So the first point of intersection will be at \(45^o\) or \(\dfrac{\pi}{4}\). As I've drawn in the picture, see how the y and x lengths are the same? That means the sine and cosine will be the same there.

Is this too confusing for you? Should we approach it a different way? :o