1. The problem statement, all variables and given/known data Find the total length of the cardioid r=a(1-cos theta) 2. Relevant equations ds2=r2dtheta2+dr2 ds= integral from beta to alpha sqrt[r2 + (dr/d theta)2]dtheta 3. The attempt at a solution dr=a(sin theta)d theta ds2=a2(1-cos theta)2d theta2 + a2sin2theta (d theta2), which reduces to: ds=21/2a(1-cos theta)1/2(d theta) I'm good up to this point. My book says that the above equation for ds simplifies to: 2a|sin1/2theta|d theta I don't see how to arrive at this simplification. Can someone please explain? Many thanks.