Half Indentify Angle and Chain Rule

[Guest]

Please help with these problem:
1. Use a half angle identity to remove the square and use the chain rule to find
Integral cos^2(2x)dx

2. If dy/dx=sin(x), and we find the slope field, where will the tangent lines be horizontal on the interval from x=0 to x=2pi.



I don't know where to start with this!

 

[jolly]

Double post.

http://www.freemathhelp.com/forum/viewt ... ght=#49969

 

[skeeter]

1. Use a half angle identity to remove the square and use the chain rule to find
Integral cos^2(2x)dx

cos^2(u) = (1/2)[1 + cos(2u)]

2. If dy/dx=sin(x), and we find the slope field, where will the tangent lines be horizontal on the interval from x=0 to x=2pi.

the slope field lines will be horizontal when dy/dx = 0, or when sin(x) = 0
since dy/dx = sin(x)
now, you answer the question ... at what values of x in the interval [0, 2pi] is
sin(x) = 0 ???

 

[Guest]

okay, Skeeter!
Im thinking that sin(x) will be pi.
also, x=0, x=pi, x=2pi