document.write( "Question 1102813: The equation r^2 = 4cos2θ is of the form r^2 = a^2 cos2θ, so the graph is a lemniscate. What is the length of each loop? At what values of θ do the endpoints of each loop occur? Sketch the graph of r^2 = 4cos2θ.\r
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Algebra.Com's Answer #717541 by KMST(5328) $\"\"$ $\"About$

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it must be $\"cos%282theta%29%3E=0\"$ , so $\"-pi%2F2%3C=2theta%3C=pi%2F2\"$ <--> $\"-pi%2F4%3C=theta%3C=pi%2F4\"$ .
\n" ); document.write( "That means that the $\"r%3E0\"$ part of the curve stays within
\n" ); document.write( "a $\"pi%2F4\"$ angle from the horizontal x-axis.
\n" ); document.write( "As $\"cos%28anything%29%3C=1\"$ , $\"r%5E2=4cos%282theta%29%3C=4\"$ ,
\n" ); document.write( "and only for $\"theta=0\"$ is
\n" ); document.write( " $\"r%5E2=4cos%280%29=4%2A1=4\"$ and $\"abs%28r%29=2\"$ .
\n" ); document.write( "The endpoints of each loop occur for $\"theta=0\"$ , with $\"r=+%22+%22+%2B-+2\"$ .
\n" ); document.write( "For all other possible values of $\"theta\"$ ,
\n" ); document.write( " $\"0%3C=cos%282theta%29%3C1\"$ , so $\"0%3C=r%5E2%3C4\"$ , and $\"0%3C=abs%28r%29%3C2\"$ .
\n" ); document.write( "As $\"theta\"$ approaches $\"%22+%22+%2B-+pi%2F4\"$ ,
\n" ); document.write( " $\"2theta\"$ approaches $\"%22+%22+%2B-+pi%2F2\"$ ,
\n" ); document.write( "and $\"r%5E2=4cos%282theta%29\"$ approaches $\"0\"$ .
\n" ); document.write( "The curve looks like an $\"infinity\"$ symbol centered at the origin,
\n" ); document.write( "tangent to the slanted lines $\"y=%22+%22+%2B-+x\"$ .
\n" ); document.write( "For a better sketch, tabulate some $\"theta\"$ , $\"r\"$ , $\"x\"$ , and $\"y\"$ values, like
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