{"text_format":"3","workbook":"xlsx","n_sheets":3,"sheets":["Sheet1","Sheet2","Sheet3"],"not_rendered":{"charts":1,"images":2,"macros":1,"defined_names":7,"comments":1},"read":"whole","date_system":"1900"}

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["       Approximating Polar Coordinate"]
["     Curves With Newton Interpolation"]
[]
[null,"   This graphing utility produces the graph "]
[null,"         of any polar coordinate function"]
[null,null,"               r = f(Q)"]
[null,"  and its Newton Interpolating Polynomials"]
[null,"  on any interval from Q = a  to  Q = b."]
[]
["Enter the function  in terms of Q:  r = f(Q) =",{"$nulls":4},"(sin(Q))^4+(cos(Q))^2"]
[]
[]
["Now enter the interval for Q (in radians):  "]
[null,"   Starting angle a =",null,-3]
[null,"    Ending angle b =",null,3]
[]
[]
["Select the degree n (1 to 6) for the interpolating polynomial:  ",{"$nulls":7},"The graph of the polar function r =",{"$nulls":4},{"$f":"F10","v":"(sin(Q))^4+(cos(Q))^2"}]
[null,6,null,null,"n =",{"$f":"B19","v":6},{"$nulls":3},"and the Newton Interpolating Polynomial"]
[]
[{"$nulls":8},"Now trace along the two curves:"]
[{"$nulls":8},"Q =",{"$f":"Sheet1!D14+K22*Sheet2!B12","v":-1.4477611940298507},52]
[{"$nulls":8},"r =",{"$f":"LOOKUP(J22,Sheet2!C3:C204,Sheet2!D3:D204)","v":0.9914167393082937}]
["Click each item below for suggestions and investigations",{"$nulls":7},"r =",{"$f":"LOOKUP(J22,Sheet2!C3:C204,Sheet2!Y3:Y204)","v":{"v":0.7253580610829317,"d":"0.725"}}]
[null,null,"   Item 1"]
[null,null,"   Item 2"]
[null,null,"   Item 3"]
[null,null,"   Item 4"]
[null,null,"   Item 5"]
[]
[]
[]
["To access/download all the DIGMath Apps for Numerical Analysis"]
["      Click this link:",null,"DIGMath Modules for Numerical Analysis"]
[]
["Created by:  Sheldon P. Gordon   "]
["                      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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["delta Q = ",{"$f":"(Sheet1!D15-Sheet1!D14)/201","v":0.029850746268656716},{"$f":"C11+Sheet2!B$12","v":-2.7313432835820888},0.8662320616833948,-0.7943533319447204,-0.3454862786227345,null,"End line",{"$nulls":10},0.947257170465181,0.9413478981099969,0.9532581046659392,0.9878569880334739,1.0531787930792051,1.1561987542707315,1.1561987542707315,-1.0602589923310572,-0.4611360195845932]
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["dQQ =",{"$f":"(Sheet1!D15-Sheet1!D14)/n","v":1},{"$f":"C13+Sheet2!B$12","v":-2.671641791044775},0.836985882937031,-0.7462486960084861,-0.3790227591339542,null,{"$f":"1.2*D204*COS(C204)","v":-1.164803484536235},{"$f":"1.2*D204*SIN(C204)+1","v":1.166038710081501},{"$nulls":9},0.9398739317148742,0.9332410749896676,0.9461486880059597,0.9828254229655419,1.0509622427932002,1.157065847798459,1.157065847798459,-1.031628964978032,-0.5239685627591806]
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["Q00 =",{"$f":"QMin","v":-3},{"$f":"C15+Sheet2!B$12","v":-2.6119402985074616},0.8098973013579482,-0.6989274120625705,-0.4091871349571063,{"$nulls":12},0.9324906929645675,0.925348647238234,0.9387507727012543,0.9759816635090068,1.0440233201804812,1.1486246729739418,1.1486246729739418,-0.9912432956213539,-0.5803235030999623]
["Q01 =",{"$f":"B16+dQQ","v":-2},{"$f":"C16+Sheet2!B$12","v":-2.5820895522388048},0.7976498143042597,-0.6760233347695084,-0.4233647093307769,null,"Approx Point",{"$nulls":10},0.9287990735894142,0.9214828316258529,0.9349575973352852,0.9719624794833917,1.0390321777991343,1.1414719657739252,1.1414719657739252,-0.9674191242951238,-0.6058535190917396]
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