Can the Length of a Curve be Simplified Using Trigonometric Identities?

[MozAngeles]

Homework Statement

length of curve r=(1+cos(2 theta))^(1/2) from -pi/2..pi/2

Homework Equations

L= integral sqrt(r²+(dr/d(theta))²

dr/d(theta)= -sin(2theta)-sin(2theta)cos(2theta)

The Attempt at a Solution

this integral seems ways to complicated is there something to simplify it?

dr/d(theta)= -sin(2theta)-sin(2theta)cos(2theta)
then squaring it and adding (1+cos(2 theta))
seems really hard to integrate. So if someone could point out what I'm doing wrong, that would be nice. thanks.

 

[epenguin]

When you see cos 2θ that should remind you of something - if not look up a table of trig identities, or even work it out - and I think you can simplify this problem.