SOLUTION: 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
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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.
https://www.dropbox.com/s/0q9rpf0ywzip2tx/Screen%20Shot%202017-11-21%20at%209.17.53%20AM.png?dl=0
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
it must be , so <--> .
That means that the part of the curve stays within
a angle from the horizontal x-axis.
As , ,
and only for is
and .
The endpoints of each loop occur for , with .
For all other possible values of ,
, so , and .
As approaches ,
approaches ,
and approaches .
The curve looks like an symbol centered at the origin,
tangent to the slanted lines .
For a better sketch, tabulate some , , , and values, like
.
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