Chapter 7: Additional Applications of Integration
Section 7.1: Polar Coordinates
Graph the parabola r=11−sinθ.
Figure 7.1.13(a) shows a naive attempt to use Maple for graphing the parabola r=1/1−sinθ. The domain is taken as θ∈−5,1, an interval containing θ=−3 π/2 at which the denominator of r becomes zero. The domain for θ in Figure 7.1.13(b) is the interval −4,0.845, a proper subinterval of −3 π/2,π/2. As θ approaches either endpoint of this larger interval, r→∞. Figure 7.1.13(a) could be "fixed" by including a view option that limits the window in which the graph is displayed. However, it is probably more appropriate to correct the graph by attending to the mathematical requisites as per Figure 7.1.13(b).
Figure 7.1.13(a) Naive polar graph of parabola
Figure 7.1.13(b) Parabola r=1/1−sinθ
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