I must find the area of the region that lies inside the first curve and outside the second curve for:
$ r^2 = 8cos2\theta, r = 2$
How do I find $a$ and $b$? My solution manual tells me that the curves intersect when $cos2\theta = 1/2$ but I don't see where that came from. I tried setting it equal to each other, but keep getting $1/4$.
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$\begingroup$The curves will intersect if $8\cos2\theta$ is positive (since it equals $r^2$) and equals 4 (because $r=2$ so $r^2=2^2=4$).
[I emphasize that it must be positive, because for example $r=8\cos2\theta$ and $r=2$ intersect whenever $8\cos2\theta=2$ and also when $8\cos2\theta=-2$.]
Anyway, $8\cos2\theta=4$ gives us $\cos2\theta=4/8=1/2$. This gives us the needed values of $\theta$.
$\endgroup$ 1 $\begingroup$my answer for this is like this,,
since r^2=8cosθ , a graph of this is lemniscate! *symmetric wrt x-axis.
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