Enhanced butterfly curve The butterfly curve of Example 8
Chapter 8, Problem 99E(choose chapter or problem)
The butterfly curve of Example 8 may be enhanced by adding a term:
\(r=e^{\sin \theta}-2 \cos 4\theta+\sin^5(\theta/12),\ \ \ \ \ \text{for}\ 0\ \leq\ \theta\ \leq\ 24\pi.\)
a. Graph the curve.
b. Explain why the new term produces the observed effect.
(Source: S. Wagon and E. Packel, Animating Calculus, Freeman,
New York, 1994)
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