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Problems include identifying curve types for given polar graphs and analyzing polar equations over a given interval by locating where r equals zero, determining the maximum r value and the angle values where it occurs, and sketching the resulting 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properties are students asked to determine for each polar graph?","Question",{"text":63,"@type":64},"Students classify the curve and determine whether the graph is symmetric about the origin, the polar axis, and a given line (an angle line).","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"What tasks are required when analyzing a polar equation over a given interval?",{"text":68,"@type":64},"Students classify the curve, check symmetry about the origin and polar axis (and a specified line), find where r is zero, find the maximum r value and the angles where it occurs, and sketch the graph.",{"name":70,"@type":61,"acceptedAnswer":71},"How does the worksheet guide determining r=0 and the maximum r value?",{"text":72,"@type":64},"For each polar equation problem, the worksheet requires evaluating the polar behavior to locate angles where r equals zero, then identifying the greatest r value within the interval and the angle(s) where that maximum 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polar graph. Classify the curve; and determine if the graph is symmetric with respect to the origin, polar axis, and line 􀁔 =􀁓/􀀕 .  \n1)    \n􀁓  \n􀀖  􀀖􀁓  􀀖􀀕  \n3)    \n􀁓  \n􀀖  􀀖􀁓  􀀖􀀕  \n2)    \n􀁓  \n􀀖  􀀖􀁓  􀀖􀀕  \n4)    \n􀁓  \n􀀖  􀀖􀁓  􀀖􀀕  \nConsider each polar equation over the given interval. Classify the curve; determine if the graph is symmetric with respect to the origin, polar axis, and line 􀁔 =􀁓/􀀕 ; find the values of 􀁔 where r is zero; find the maximum  r  value and the values of 􀁔 where this occurs; and sketch the graph.  \n5) r 􀀠 􀀙sin (􀀖􀁔), 0 ≤ 􀁔 \u003C 􀁓  \n􀁓  \n􀀖  􀀖􀁓  􀀖􀀕  \n6) r􀀕 􀀠 􀀖􀀙 cos (􀀕􀁔), 0 ≤ 􀁔 \u003C 􀀕􀁓􀁓  \n􀀖 􀀖􀁓 􀀖  \n􀀕  \nKuta Software-Infinite Precalculus Graphs of Polar Equations  \nName  Date  Period   \nConsider each polar graph. Classify the curve; and determine if the graph is symmetric with respect to the origin, polar axis, and line 􀁔 =􀁓/􀀕 .  \n1)    \n􀁓  \n􀀖  􀀖􀁓  􀀖􀀕  \nRose  \nSymmetric about the polar axis  \n3)    \n􀁓  \n􀀖 􀀖􀁓 􀀖  \n􀀕  \nLemniscate  \nSymmetric about the origin  \n2)    \n􀁓  \n􀀖  􀀖􀁓  􀀖􀀕  \nLooped limaçon  \nSymmetric about the line 􀁔 = ~~ ~~  \n4)    \n􀁓  \n􀀖 􀀖􀁓 􀀖  \n􀀕  \nDimpled limaçon  \nSymmetric about the polar axis  \nConsider each polar equation over the given interval. Classify the curve; determine if the graph is symmetric with respect to the origin, polar axis, and line 􀁔 =􀁓/􀀕 ; find the values of 􀁔 where r is zero; find the maximum  r  value and the values of 􀁔 where this occurs; and sketch the graph.  \n5) r 􀀠 􀀙sin (􀀖􀁔), 0 ≤ 􀁔 \u003C 􀁓  \nRose  \nSymmetric about the line 􀁔 =  \nr 􀀠 􀀓 when 􀁔 = 􀁞 􀀓 , ~~ ~~~~ ~~, 􀀕􀁓􀀖~~ ~~􀁠  \n r  􀀠 􀀙 when 􀁔 = 􀁞 ~~ ~~~~ ~~, ~~ ~~, ~~ ~~􀀘~~ ~~􀁠  \n 􀁓   \n􀀕  \n6) r􀀕 􀀠 􀀖􀀙 cos (􀀕􀁔), 0 ≤ 􀁔 \u003C 􀀕􀁓  \nLemniscate  \nSymmetric about the the origin, polar axis, and line 􀁔 = ~~ ~~  \nr 􀀠 􀀓 when 􀁔 = 􀁞 ~~ ~~~~ ~~, ~~ ~~􀀖􀁓􀀗~~ ~~, ~~ ~~􀀘􀁓􀀗~~ ~~, ~~ ~~􀀚􀁓􀀗~~ ~~􀁠  \n r  􀀠 􀀙 when 􀁔 = 􀁞􀀓 , 􀁓 􀁠  \nCreate your own worksheets like this one with Infinite Precalculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaipfjkoQvQtZo","https://ap.wps.com/l/cbCaipfjkoQvQtZo","pdf",143602,"English","# Polar Graph Classification\n## Symmetry tests for polar graphs\n# Polar Equation Analysis\n## Curve classification over an interval\n## Finding where r is zero\n## Maximum r value and corresponding angles\n## Sketching the polar graph","[{\"question\":\"What properties are students asked to determine for each polar graph?\",\"answer\":\"Students classify the curve and determine whether the graph is symmetric about the origin, the polar axis, and a given line (an angle line).\"},{\"question\":\"What tasks are required when analyzing a polar equation over a given interval?\",\"answer\":\"Students classify the curve, check symmetry about the origin and polar axis (and a specified line), find where r is zero, find the maximum r value and the angles where it occurs, and sketch the graph.\"},{\"question\":\"How does the worksheet guide determining r=0 and the maximum r value?\",\"answer\":\"For each polar equation problem, the worksheet requires evaluating the polar behavior to locate angles where r equals zero, then identifying the greatest r value within the interval and the angle(s) where that maximum happens.\"}]","Infinite Precalculus - Graphs of Polar Equations - Worksheet | PDF",1791426979]