{"text_format":"3","workbook":"xlsx","n_sheets":3,"sheets":["Sheet1","Sheet2","Sheet3"],"not_rendered":{"charts":1,"images":2,"macros":1,"external_links":1,"defined_names":27,"comments":1},"read":"whole","date_system":"1900"}

{"sheet":"Sheet1","index":0,"n_rows":47,"n_cols":29,"rows_kept":47,"merged":[[40,2,40,3]]}
["         Approximating Polar Coordinate",{"$nulls":24},{"$f":"n+1","v":4},null,null,{"$f":"n+1","v":4}]
["     Curves With Lagrange Interpolation"]
[]
[null,"    This graphing utility produces the graph "]
[null,"         of any polar coordinate function"]
[null,null,"               r = f(Q)"]
[null,"  and its Lagrange Interpolating Polynomials"]
[null,"    on any interval from Q = a  to  Q = b."]
[]
["Enter the function  in terms of Q:  r = f(Q) =",{"$nulls":4},"(sin(Q))^2+(cos(Q))^4"]
[]
[]
["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},{"$f":"F10","v":"(sin(Q))^2+(cos(Q))^4"}]
[null,3,null,"n =",{"$f":"B19","v":3}]
[]
[{"$nulls":8},"Now trace along the two curves:"]
[{"$f":"\"Enter the \" & TEXT(n+1,\"0\")& \" different interpolating points between  \"&TEXT(QMin,\"##.#\") & \" and \"& TEXT(QMax, \"#.#\")","v":"Enter the 4 different interpolating points between  -3. and 3."},{"$nulls":7},"Q =",{"$f":"Sheet1!D14+K22*Sheet2!B12","v":0.5223880597014925},118]
[1,-3,{"$f":"IF(Z23=0,\"That's outside the interval\",\"\")","v":""},{"$nulls":5},"r =",{"$f":"LOOKUP(J22,Sheet2!C3:C204,Sheet2!D3:D204)","v":0.8263972166167834},{"$nulls":15},{"$f":"IF(OR(B23<QMin,B23>QMax),0,1)","v":1}]
[2,1,{"$f":"IF(Z24=0,\"That's outside the interval\",\"\")","v":""},{"$nulls":5},"r =",{"$f":"LOOKUP(J22,Sheet2!C3:C204,Sheet2!T3:T204)","v":{"v":0.8684075629210863,"d":"0.868"}},{"$nulls":15},1]
[3,2,{"$f":"IF(AND(A25<=n+1,Z25=0),\"That's outside the interval\",IF(A25>n+1,\"\",\"\"))","v":""},{"$nulls":22},1]
[4,-1,{"$f":"IF(AND(A26<=n+1,Z26=0),\"That's outside the interval\",IF(A26>n+1,\"\",\"\"))","v":""},{"$nulls":22},1]
[5,0,{"$f":"IF(AND(A27<=n+1,Z27=0),\"That's outside the interval\",IF(A27>n+1,\"\",\"\"))","v":""},{"$nulls":22},1]
[6,5,{"$f":"IF(AND(A28<=n+1,Z28=0),\"That's outside the interval\",IF(A28>n+1,\"\",\"\"))","v":""},{"$nulls":22},0]
[7,-0.5,{"$f":"IF(AND(A29<=n+1,Z29=0),\"That's outside the interval\",IF(A29>n+1,\"\",\"\"))","v":""},{"$nulls":22},1]
[{"$nulls":25},1]
["Click each item below for suggestions and investigations"]
[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 Calculus"]
["     Click this link:",null,"DIGMath for Calculus"]
[]
["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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[null,null,"Q","r = f(Q)","x","y",null,"Tracing point",null,null,{"$f":"QMin","v":-3},{"$f":"r0","v":0.9804817448415614},null,"linear","quad","cubic","quartic","quintic","6th","interpol","x","y"]
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["delta Q = ",{"$f":"(Sheet1!D15-Sheet1!D14)/201","v":0.029850746268656716},{"$f":"C11+Sheet2!B$12","v":-2.7313432835820888},0.8662320616833947,-0.7943533319447202,-0.3454862786227345,null,"End line",{"$nulls":5},0.9469556796267231,0.9285255842548458,0.9116708355270207,0.8872839122976174,0.8458476592672576,0.7787282787359795,0.9116708355270207,-0.8360216596351345,-0.3636089891235519]
[null,null,{"$f":"C12+Sheet2!B$12","v":-2.701492537313432},0.851441232208327,-0.7703065587025577,-0.3627395450240535,null,0,0,{"$nulls":4},0.9432305612695189,0.9232491110683587,0.9051753228150595,0.8792090715913808,0.8353191445975781,0.7645187207032557,0.9051753228150595,-0.8189202748987168,-0.3856318819718586]
["dQQ =",{"$f":"(Sheet1!D15-Sheet1!D14)/(n+1)","v":1.5},{"$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":4},0.9395054429123146,0.9180719245909461,0.8988989230326356,0.8715491589012183,0.8255627578168853,0.7516879274582836,0.8988989230326356,-0.8014497769098016,-0.4070596134725986]
[null,null,{"$f":"C14+Sheet2!B$12","v":-2.6417910447761184},0.823071860098904,-0.7223917828835706,-0.3944583614387783,{"$nulls":7},0.9357803245551103,0.9129940248226073,0.8928386591307942,0.864293311573523,0.8165492484150008,0.7401700669494123,0.8928386591307942,-0.7836245436933872,-0.42789419925935573]
["Q00 =",{"$f":"Sheet1!B23","v":-3},{"$f":"C15+Sheet2!B$12","v":-2.6119402985074616},0.8098973013579482,-0.6989274120625705,-0.4091871349571063,{"$nulls":7},0.932055206197906,0.9080154117633427,0.8869915540605795,0.8574307885054346,0.8082499687957144,0.7299011686943994,0.8869915540605795,-0.765458423384626,-0.44813772329979606]
["Q01 =",{"$f":"Sheet1!B24","v":1},{"$f":"C16+Sheet2!B$12","v":-2.5820895522388048},0.7976498143042596,-0.6760233347695083,-0.42336470933077686,null,"Approx Point",{"$nulls":5},0.9283300878407019,0.9031360854131523,0.881354630773036,0.8509509701448384,0.8006368688984232,0.7208190937765145,0.881354630773036,-0.7469647531096463,-0.4677923073297805]
["Q02 =",{"$f":"Sheet1!B25","v":2},{"$f":"C17+Sheet2!B$12","v":-2.552238805970148},0.7865038048952644,-0.6538206127028698,-0.4371576849599835,null,0,0,{"$nulls":4},0.9246049694834977,0.8983560457720358,0.8759249122192082,0.8448433584903648,0.7936824908197725,0.7128635050564295,0.8759249122192082,-0.7281563791864097,-0.4868600818473057]
["Q03 =",{"$f":"Sheet1!B26","v":-1},{"$f":"C18+Sheet2!B$12","v":-2.522388059701491},0.7766179938900795,-0.6324313752303955,-0.450739463612897,null,{"$f":"Sheet1!J24*COS(Sheet1!J22)","v":0.7525881564211155},{"$f":"Sheet1!J24*SIN(Sheet1!J22)","v":0.4332929288059142},{"$nulls":4},0.9208798511262934,0.8936752928399934,0.8706994213501396,0.8390975770913914,0.7873599634352932,0.7059758375998825,0.8706994213501396,-0.7090456785562415,-0.5053431587151318]
["Q04 =",{"$f":"Sheet1!B27","v":0},{"$f":"C19+Sheet2!B$12","v":-2.4925373134328344},0.7681331566433338,-0.6119372263333044,-0.4642858789176714,{"$nulls":7},0.9171547327690892,0.8890938266170251,0.8656751811168756,0.8337033710480416,0.7816429970210468,0.7000992693211169,0.8656751811168756,-0.6896445813550719,-0.5232436054165622]
["Q05 =",{"$f":"Sheet1!B28","v":5},{"$f":"C20+Sheet2!B$12","v":-2.4626865671641776},0.7611701184440948,-0.5923883314303403,-0.4779707250422085,{"$nulls":7},0.913429614411885,0.884611647103131,0.86084921447046,0.8286506070111854,0.7765058778752613,0.6951786918420993,0.86084921447046,-0.6699645945320035,-0.5405634210043964]
["Q06 =",{"$f":"Sheet1!B29","v":-0.5},{"$f":"C21+Sheet2!B$12","v":-2.4328358208955208},0.7558280339465708,-0.5738031991733802,-0.4919612845722038,{"$nulls":7},0.9097044960546807,0.8802287542983109,0.8562185443619378,0.8239292731824378,0.7719234629399718,0.6911606815675138,0.8562185443619378,-0.650016826421636,-0.5573045137786166]
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