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Pre-Calculus Practice Problem 215

# Pre-Calculus Practice Problem 215 - What changes are there...

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Unit 6, Activity 8, The Graphs of Polar Functions with Answers Blackline Masters, Advanced Math - Pre-Calculus Page Louisiana Comprehensive Curriculum, Revised 2008 213 I. The Equation r=asin(n θ ) r=acos(n θ ) Number of Petals Domain Number of Zeros Symmetry Maximum r- values r= sin2 θ 4 [0, 2 π ] 5 with respect to the pole 1 r = sin3 θ 3 [0, π ] 4 with respect to the pole 1 r = sin4 θ 8 [0, 2 π ] 9 with respect to the pole 1 r = sin5 θ 5 [0, π ] 6 with respect to the pole 1 r = cos2 θ 4 [0, 2 π ] 5 with respect to the polar axis 1 r = cos3 θ 3 [0, π ] 4 with respect to the polar axis 1 r = cos4 θ 8 [0, 2 π ] 9 with respect to the polar axis 1 r = cos5 θ 5 [0, π ] 6 with respect to the polar axis 1 II. Writing exercise 1. In each of the problems above a = 1. Let a take on other values.
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Unformatted text preview: What changes are there as far as the table is concerned? The maximum r-values change and reflect the value of a. 2. What in general can you say about the value of n ? If n is odd then the number of petals is equal to n. If n is even the number of petals is equal to 2n. 3. What do you see with the symmetry of each graph? Is there a pattern? All of the sine graphs have the same symmetry as do the cosine graphs. 4. What is the least domain needed for a complete graph? Is it the same for all of the rose curves? When n is odd the graph can be completed in [0, π ]. When n is even then the graph is completed in [0, 2 π ] 5. Is there a pattern with the zeros? The number of zeros is 1 more than the number of petals....
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