Chapter 10.3, Problem 56ES

(a) (Figure 3.1.3a). What is the area that is enclosed by one petal of the rose $r=a\cos n\theta$ if $n$ is an even integer?

(b) What is the area that is enclosed by one petal of the rose $r=a\cos n\theta$ if $n$ is an odd integer?

(c) Use a CAS to show that the total area enclosed by the rose $r=a\cos n\theta \text{is}\pi a^2/2$ if the number of petals is even.

(d) Use a CAS to show that the total area enclosed by the rose $r=a\cos n\theta \text{ is }\pi a^2/4$ if the number of petals is odd.