Reference question:
Based on the results in Exercise 73, fill in the blank(s) to correctly complete each sentence.
(a) The graph of r = f(θ) is symmetric with respect to the polar axis if substitution of__________for θ leads to an equivalent equation.
(b) The graph of r = f(θ) is symmetric with respect to the vertical line
(c) Alternatively, the graph of r = f(θ) is symmetric with respect to the vertical line
(d) The graph of r = f(θ) is symmetric with respect to the pole if substitution of_________for r leads to an equivalent equation.
(e) Alternatively, the graph of r = f(θ) is symmetric with respect to the pole if substitution of________for θ leads to an equivalent equation.
(f) In general, the completed statements in parts (a)–(e) mean that the graphs of polar equations of the form r = a ± b cos θ (where a may be 0) are symmetric with respect to_______.
(g) In general, the completed statements in parts (a)–(e) mean that the graphs of polar equations of the form r = a ± b sin θ (where a may be 0) are symmetric with respect to_______.
Reference question:
Concept CheckThe polar graphs in this section exhibit symmetry. Visualize an xy-plane superimposed on the polar
Complete the missing ordered pairs in the graphs below.
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Trigonometry (11th Edition)
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