Find the areas bounded by 4 equations

[tony873004]

Homework Statement

I won't post the entire problem since I'm only stuck on one part of it. I need to find where y=cos x and y=sin 2x intersect.

Homework Equations

sin(x)=cos(x +- pi/2)

The Attempt at a Solution

cos x = sin 2x

since sin(x)=cos(x +- pi/2), sin 2x = sin(x+pi/2), therefore, 2x=x+pi/2. This gives me 1/2 pi, which is 1 of the intersection points. And of course, any point 2pi away from this is another intersection point. But how do I find the other intersection point? The one that the graph shows to be at about 0.53.

 

[rock.freak667]

sin2x =2sinxcosx (Double angle formula)