Chapter 7: Additional Applications of Integration
Section 7.1: Polar Coordinates
Graph the roses r=cos5 θ and r=cosθ/5.
The rose r=cos5 θ is graphed in Figure 7.1.9(a); the rose r=cosθ/5, in Figure 7.1.9(b). The rose r=cos5 θ is drawn with θ∈0,π; the rose r=cosθ/5, with θ∈0,5 π.
Figure 7.1.9(a) The rose r=cos5 θ
Figure 7.1.9(b) The rose r=cosθ/5
The rose in Figure 7.1.9(a) with its five "petals" meets expectations for a flower-like shape, but the rose in Figure 7.1.9(b) is certainly a surprise. Indeed, the rose r=cosθ/3 is a translation of the limaçon r=1/2+cosθ.
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