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["     Taylor Approximations to Polar Curves"]
[]
[null,"      This graphing utility produces the graphs"]
[null,"                  of any polar curve based on "]
[null,null,"                  r = f(Q)    "]
[null," and the curve for the Taylor polynomial based on",{"$nulls":4}," "]
[null,null,"                 r = g(Q) "]
[null,"         on any interval from Q = a  to Q = b."]
[]
["Enter the f(Q) function in terms of Q:   r = f(Q) =  ",{"$nulls":4},"sin(Q)"]
[]
[]
["Enter the Taylor approximation to f in terms of Q:    "]
[{"$nulls":4},"  r = g(Q) =  ","Q-Q^3/6+Q^5/120 "]
[]
[]
[]
["Now enter the interval for Q:  "]
[null,"Starting value Q = a =",null,-2]
[null,"Ending value Q = b =",null,3]
[]
[]
[{"$nulls":8},"The graph of the polar function"]
[{"$nulls":9},"r =",{"$f":"F10","v":"sin(Q)"}]
[]
["Click each item below for suggestions and investigations"]
[null,null,"   Item 1",{"$nulls":5},"Now trace along the polar curve:"]
[null,null,"   Item 2",{"$nulls":5},"Q  = ",{"$f":"D19+K28*Sheet2!B12","v":{"v":-1.8602794411177646,"d":"-1.860"}},14]
[null,null,"   Item 3",{"$nulls":5},"r =",{"$f":"LOOKUP(J28,Sheet2!C3:C504,Sheet2!D3:D504)","v":{"v":-0.9554950002214384,"d":"-0.955"}}]
[]
[{"$nulls":8},"Along the approximating Taylor function:"]
[{"$nulls":8},"r =",{"$f":"LOOKUP($J28,Sheet2!C3:C503,Sheet2!G3:G503)","v":{"v":-0.9706286321814167,"d":"-0.971"}}]
["To access/download all the DIGMath Apps for Numerical Analysis"]
["Click this link:",null,"https://we-dig-math.org/dynamic-numerical-analysis.htm"]
[]
["Created by:  Sheldon P. Gordon    © 2026"]
["                      Farmingdale State College    "]
["Development of this module was supported by the "]
["NSF's Division of Undergraduate Education  "]
["under grants DUE-0310123 and DUE-0442160."]

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[null,null,"Q","r = f(Q)","x","y","r = g(Q)","x","y",null,"Tracing point"]
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