{"text_format":"3","workbook":"xlsx","n_sheets":3,"sheets":["Sheet1","Sheet2","Sheet3"],"not_rendered":{"charts":1,"images":1,"macros":1,"defined_names":6,"comments":1},"read":"whole","date_system":"1900"}

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[null,"      Slopes of Polar Curves"]
[]
[null,"   This graphing utility produces the graph "]
[null,"       of any polar coordinate function"]
[{"$nulls":3},"r = f(Q)"]
[null,"   along with the tangent line to the curve"]
[null,"  on any interval from Q = a  to Q = b."]
[]
["Enter the function  in terms of Q:  r = f(Q) =",{"$nulls":4},"(sin(Q))^4+(cos(Q))^2"]
[]
[]
["Now enter the interval for Q (in radians):  "]
[null,"   Starting angle a =",null,-6.28]
[null,"    Ending angle b =",null,6.28]
[]
[]
[]
[]
[{"$nulls":8},"The graph of the polar function r =",{"$nulls":4},{"$f":"F9","v":"(sin(Q))^4+(cos(Q))^2"}]
["Click each item below for suggestions and investigations"]
[null,null,"   Item 1"]
[null,null,"   Item 2",{"$nulls":5},"Now trace along the polar curve:"]
[null,null,"   Item 3",{"$nulls":5},"Q =",{"$f":"Sheet1!D13+K23*Sheet2!B12","v":0.46865671641791007},108]
[null,null,"   Item 4",{"$nulls":5},"r =",{"$f":"LOOKUP(J23,Sheet2!C3:C204,Sheet2!D3:D204)","v":0.8376028146014278}]
[]
[{"$nulls":8},"     The slope of the tangent line at Q is m =",{"$nulls":5},{"$f":"m","v":-0.6613856764037016}]
[]
["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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