Question

find the length of the polar curve r(t)=<3cost,6sint> for 0 less than or equal to (t) less than or equal to 2pi

Answer 1

do you know the formula for polar arc length?

Answer 2

yeah i'm just confused towards the end when you have radical 2+2costheta. not sure how to simplify from there

Answer 3

sorry I'm a bit rusty and I'm not getting the same thing, can you show me how you got that?

Answer 4

r=1+costheta
f'(theta)=-sintheta
using the formula:
radical (1+costheta)^2+(-sintheta)^2)dtheta
simplify to radical (cos^2theta + 2costheta +sin^2theta)dtheta
use sin^2theta +cos^2theta=1 to further simplify:
radical(1+2costheta +cos^2theta +sin^2theta)dtheta
becomes radical (2+2costheta)

Answer 5

i think i'm supposed to use the fact that 1-costheta is = 2sin^2(theta/2) but i'm not sure how that applies since its positive

Answer 6

how did you get r = 1 + cosΘ ??

Answer 7

Though you can change to polar form but why spend extra effect when you can just use arc-length formula in parametric form

Answer 8

*effort*

Answer 9

i mistyped the entire problem, sorry the original question is find the arc length for the polar curve r=1+costheta