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File:PolarArclength.png - Revision history
2024-03-29T15:33:33Z
Revision history for this page on the wiki
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https://artofproblemsolving.com/wiki/index.php?title=File:PolarArclength.png&diff=107956&oldid=prev
Mag1c: [asy]
import graph;
size(120);
real f(real t) {return 1;}
path g=polargraph(f,pi/4,pi/3,10000, operator --);
draw(g,black);
draw((1/2,sqrt(3)/2)--(0,0)--(1/sqrt(2),1/sqrt(2)));
label("$f(\theta)d\theta$",(cos(7pi/24),sin(7pi/24)),S);
label("$f(\theta)$...
2019-07-27T04:39:25Z
<p>[asy] import graph; size(120); real f(real t) {return 1;} path g=polargraph(f,pi/4,pi/3,10000, operator --); draw(g,black); draw((1/2,sqrt(3)/2)--(0,0)--(1/sqrt(2),1/sqrt(2))); label("$f(\theta)d\theta$",(cos(7pi/24),sin(7pi/24)),S); label("$f(\theta)$...</p>
<p><b>New page</b></p><div>== Summary ==<br />
[asy]<br />
import graph;<br />
size(120);<br />
real f(real t) {return 1;}<br />
path g=polargraph(f,pi/4,pi/3,10000, operator --);<br />
draw(g,black);<br />
draw((1/2,sqrt(3)/2)--(0,0)--(1/sqrt(2),1/sqrt(2)));<br />
label("$f(\theta)d\theta$",(cos(7pi/24),sin(7pi/24)),S);<br />
label("$f(\theta)$",(1/sqrt(2)/2,1/sqrt(2)/2),E);<br />
draw((1/2,sqrt(3)/2)--(1/sqrt(2),1/sqrt(2))--(1/2-(1/sqrt(2)-sqrt(3)/2)*0.5,sqrt(3)/2-(1/2-1/sqrt(2))*0.5)--cycle,red);<br />
draw(rightanglemark((1/sqrt(2),1/sqrt(2)), (1/2,sqrt(3)/2),(1/2-(1/sqrt(2)-sqrt(3)/2)*0.5,sqrt(3)/2-(1/2-1/sqrt(2))*0.5),1.6));<br />
label("$df$", ((1/2+1/2-(1/sqrt(2)-sqrt(3)/2)*0.5)/2 ,(sqrt(3)/2+sqrt(3)/2-(1/2-1/sqrt(2))*0.5)/2 ),W);<br />
label("$ds$", ((1/sqrt(2)+1/2-(1/sqrt(2)-sqrt(3)/2)*0.5)/2 ,(1/sqrt(2)+sqrt(3)/2-(1/2-1/sqrt(2))*0.5)/2 ), NE);<br />
draw("$f(\theta+d\theta)$",(0+ (1/2-1/sqrt(2))*.8,0+ (sqrt(3)/2-1/sqrt(2))*.8 )--(1/2-(1/sqrt(2)-sqrt(3)/2)*0.5 + (1/2-1/sqrt(2))*.8,sqrt(3)/2-(1/2-1/sqrt(2))*0.5 + (sqrt(3)/2-1/sqrt(2))*.8),NW,Bars,PenMargins);<br />
draw((1,0)--(0,0)--(0,1));<br />
[/asy]</div>
Mag1c