Find the length of the curve with the given parametric equations
(a) x = sin θ, y = cos θ for θ ‰¤ θ ‰¤ 2Ï€
(b) x = sin 3θ, y = cos 3θ for 0 ‰¤ θ ‰¤ 2Ï€
(c) Explain why the lengths in parts (a) and (b) are not equal
You can generate surfaces by revolving smooth curves, given parametrically, about a coordinate axis As t increases from a to b, a smooth nave x = F(t) and y = G(t) is traced out exactly once. Revolving this curve about the x-axis for y ‰¥ 0 gives the surface of revolution with surface area

Transcribed Image Text:

2. Г 2ту. dt