{"text_format":"3","workbook":"xlsx","n_sheets":3,"sheets":["Sheet1","Sheet2","Sheet3"],"not_rendered":{"charts":1,"images":2,"macros":1,"defined_names":4,"comments":1},"read":"whole","date_system":"1900"}

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[null,"       Intersection of Curves"]
[null,"        in Polar Coordinates"]
[]
[null,"  This graphing utility lets you locate the"]
[null,null," the points of intersection"]
[null,"    of any two polar coordinate curves"]
[null,null,"r = f(Q)   and   r = g(Q)"]
[null,"  on any interval from Q = a  to Q = b."]
[]
["Enter the first function  in terms of Q:    r = f(Q) = ",{"$nulls":4},"(sin(Q))^2+(cos(Q))^4"]
[]
[]
["Enter the second function  in terms of Q:   r = g(Q) = ",{"$nulls":4},"sin(2*Q)"]
[]
["Now enter the interval for Q (in radians):  "]
[null,"   Starting angle a =",null,-3.14]
[null,"    Ending angle b =",null,3.14]
[]
[]
[]
[]
[]
["Click each item below for suggestions and investigations",{"$nulls":7},"The graphs of the polar functions r =",{"$nulls":4},{"$f":"F10","v":"(sin(Q))^2+(cos(Q))^4"}]
[null,"   Item 1",{"$nulls":9},"      and  r =",null,{"$f":"F13","v":"sin(2*Q)"}]
[null,"   Item 2"]
[null,"   Item 3",{"$nulls":6},"Now trace along the first polar curve:"]
[{"$nulls":8},"Q =",{"$f":"Sheet1!D16+K27*Sheet2!B12","v":0.1718407960199002},106]
[{"$nulls":8},"r =",{"$f":"LOOKUP(J27,Sheet2!C3:C204,Sheet2!D3:D204)","v":0.9716152204088453}]
[]
["To access/download all the DIGMath Apps for Calculus",{"$nulls":7},"Now trace along the second polar curve:"]
["     Click this link:",null,"DIGMath for Calculus",{"$nulls":5},"Q =",{"$f":"Sheet1!D16+K31*Sheet2!B12","v":-0.7654726368159204},76]
[{"$nulls":8},"r =",{"$f":"LOOKUP(J31,Sheet2!C3:C204,Sheet2!E3:E204)","v":-0.9992060518620877}]
["Created by:  Sheldon P. Gordon   "]
["                      Farmingdale State College    ",{"$nulls":7},"Be sure that both the Q and the r coordinates are the same"]
["Development of this module was supported by the ",{"$nulls":8},"for a true point of intersection in polar coordinates."]
["NSF's Division of Undergraduate Education  "]
["under grants DUE-0310123 and DUE-0442160."]

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[null,null,"Q","r = f(Q)","r = g(Q)","x1","y1","x2","y2","Tracing point"]
[]
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