SOLUTION: a. The equation r2 = 4cos2θ is of the form r^2 = a^2*cos2θ, so the graph is a lemniscate. What is the length of each loop? b. At what values of θ do the endpoints

Question 1103012: a. The equation r2 = 4cos2θ is of the form r^2 = a^2*cos2θ, so the graph is a lemniscate. What is the length of each loop?
b. At what values of θ do the endpoints of each loop occur?
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
For a lemniscate of the form,

the arc length is,
where is the gamma function.
.
.
.

So,

.
.
.
The maximum absolute value of the cosine is equal to 1 and occurs when the argument and . So then when,

and equals zero when,

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SOLUTION: a. The equation r2 = 4cos2&#952; is of the form r^2 = a^2*cos2&#952;, so the graph is a lemniscate. What is the length of each loop? b. At what values of &#952; do the endpoints

SOLUTION: a. The equation r2 = 4cos2θ is of the form r^2 = a^2*cos2θ, so the graph is a lemniscate. What is the length of each loop? b. At what values of θ do the endpoints