Parametric Equations for Polar Curves Problem: Figure 13-5o shows the ellipse with the following polar equation, superimposed on a rectangular coordinate grid: Figure 13-5o a. Confirm on your grapher that the equation gives the graph in Figure 13-5o. Note that the value of shown in the figure is 0.5 radian. b. Use the definitions of cosine and sine and the value of r from the polar equation to write parametric equations for the ellipse. Confirm that your parametric equations give the same ellipse and that tracing to = 0.5 radian gives the same point shown. c. The ellipse in Figure 13-5o has center at (4, 0), x-radius 5, and y-radius 3. Use this information to write another set of parametric equations for the ellipse in terms of the parameter t. Plot the parametric equations in part c. Does the ellipse coincide with the one shown in Figure 13-5o? Does tracing to t = 0.5 radian on this ellipse give the same point as tracing to = 0.5 radian on the polar version of the ellipse? Do your findings surprise you?

Midterm 3 Study Guide Animal Diversity and Evolution notes 3 Domains 1. Bacteria 2. Eukarya 3. Archaea Eukaryan Diversity -protists -plants -fungi -animals Choanoflagellates sister group of animals Metazoans another name for animals There are more animals than any other group. 70% of them are insects (number of species) Prokaryotes have been around longer than...