Question

Find the exact length of the curve. Use a graph to determine the parameter interval.
r = (cos(θ/2))^2

Answer 1

aren't they suppose to tell you from where to where?

Answer 2

You are suppose to find that out yourself by graphing it

Answer 3

here is the graph but you cant use it tho to determine the interval

Answer 4

https://www.google.com/#q=(cos(x%2F2))%5E2

Answer 5

oh also is this in polar? if it is in polar then i am wrong lol

Answer 6

ya it's polar

Answer 7

use this polar grapher :)

Answer 8

http://fooplot.com/#W3sidHlwZSI6MSwiZXEiOiIoY29zKHQvMikpXjIiLCJjb2xvciI6IiMwMDgwY2MiLCJ0aGV0YW1pbiI6IjAiLCJ0aGV0YW1heCI6IjJwaSIsInRoZXRhc3RlcCI6Ii4wMSJ9LHsidHlwZSI6MTAwMCwid2luZG93IjpbIi0yLjYwNTA1NTk5OTk5OTk5OSIsIjIuNzE5NzQzOTk5OTk5OTk5IiwiLTEuNzYxMjc5OTk5OTk5OTk5NSIsIjEuNTE1NTE5OTk5OTk5OTk5OCJdfV0-

this one is better it turns out that is just a circle :D use 2pi r with radius of one :)

Answer 9

@timo86m Unfortunately, it's not a circle; it's a Cardioid.

http://www.wolframalpha.com/input/?i=Polar+plot+%28cos%28t%2F2%29%29%5E2

Answer 10

I would first rewrite the function as \(\large r=\cos^2(\theta/2)=\frac{1}{2}(1+\cos\theta).\) Then recall that arclength in polar coordinates is given by
\[\large L = \int_{\theta_0}^{\theta_1} \sqrt{r^2+\left(\frac{dr}{d\theta}\right)^2}\,d\theta\] Although the wolfram alpha link shows the plot for \(\large 0\leq \theta\leq 4\pi\), it turns out that \(\large 0\leq \theta\leq2\pi\) is the smallest interval needed to plot the function. We now see that \[\large L= \int _0^{2\pi}\sqrt{r^2+\left(\frac{dr}{d\theta}\right)^2}\,d\theta\] where \(\large r=\frac{1}{2}(1+\cos(2\theta))\).

Can you take things from here? :-)

Answer 11

I get stuck at \[1/2\sqrt{(1+2\cos2\theta} +\cos(2\theta)^2 +4\sin (2\theta)^2)\]