Posted by T.Gracken on October 22, 2002 at 21:13:09:
In Reply to: Re: ok- there were a couple of extraneous steps there, but I still don't see any mistakes... posted by Joel on October 22, 2002 at 18:09:14:
: : : : : Please help me find the area of the region.
: : : : : R={(x,y)| 0<=x<=(2Pi), 0<=y<=(2Pi), [Sin(x+y)Cosy]>=(Sin x) }
: : : : sin(x+y)cos(y) >= sin(x)
: : : : (sin(x)cos(y)+cos(x)sin(y))*cos(y) >= sin(x)
: : : : sin(x)cos^2(y) + cos(x)cos(y)sin(y) >= sin(x)
: : : : cos(x)cos(y)sin(y) >= sin(x) - sin(x)cos^2(y)
: : : : (1/2)cos(x)cos(2y) >= sin(x)(1-cos^2(y)) ignore this one
: : : : (1/2)cos(x)cos(2y) >= sin(x) - sin(x)cos^2(y) ignore this one (here we are again :)
: : I don't see how you got the next line [below]. Shouldn't it be (1/2)cos(x)sin(2y) >=...?
: no change on left side; on right side substituting: cos^2(y)=(1+cos(2y))/2
I don't have a problem with the right side. How did you get the factor "cos(2y)" on the left???
: : : : (1/2)cos(x)cos(2y) >= sin(x) - sin(x)(1+cos(2y)/2
: : : : (1/2)cos(x)cos(2y) >= sin(x) - (1/2)sin(x) - (1/2)sin(x)cos(2y)
: : : : cos(x)cos(2y) + sin(x)cos(2y) >= sin(x)
: : : : (cos(2y))(sin(x)+cos(x)) >= sin(x)
: : : : cos(2y) >= (sin(x))/(sin(x)+cos(x))
: : : : y >= (1/2)arccos(sin(x)/(sin(x)+cos(x))
: : : : which is a bunch of open-ended, roughly vertical, squiggly lines if I'm not mistaken.
: : : : or did I do something illegal with a "zero" someplace?