{"text_format":"3","workbook":"xlsx","n_sheets":3,"sheets":["Sine","Tangent","Sheet2"],"not_rendered":{"charts":6,"images":6,"defined_names":30,"comments":2},"read":"whole","date_system":"1900"}

{"sheet":"Sine","index":0,"n_rows":42,"n_cols":19,"rows_kept":42}
[null,"       Visualizing Trig Substitutions"]
[]
[null,null,"    This DIGMath spreadsheet lets you"]
[null,null,"               visualize the process of"]
[null,null,"      Integration with Trig Substitutions"]
[null,null,"              for a function of the form:"]
[]
[]
[]
[]
["What is the value of the constant a?",null,null,3]
[]
["What is the value of the constant b?",null,null,2]
[{"$nulls":9},"Pick a tracing point x0 =",null,null,{"$f":"a+K15*dx","v":0.5}]
["           Your subsitution is then x = ",null,null,{"$f":"TEXT(a0/b0,\"0.00\")","v":"1.50"},{"$nulls":6},150]
[null,null,"          so that   dx  =",{"$f":"TEXT(a0/b0,\"0.00\")","v":"1.50"}]
[{"$nulls":9},"The corresponding transformed point is ",{"$nulls":5},{"$f":"LOOKUP(x0,Sheet2!C3:C202,Sheet2!F3:F202)","v":0.33277459985167746},"= q"]
["What is the interval for x for display?  ",null,null,{"$f":"\"  It must be within \"&TEXT(-a0/b0,\"0.00\")& \" to \"&TEXT(a0/b0,\"0.00\")","v":"  It must be within -1.50 to 1.50"}]
[null,null,"xMin =",-1,{"$f":"IF(a<-a0/b0,\"Must be larger than \"&TEXT(-a0/b0,\"0.00\"),\"\")","v":""},{"$nulls":4}," The area from x =",null,{"$f":"a","v":-1},"to x =",{"$f":"x0","v":0.5},"=",{"$f":"LOOKUP(x0+dx/2,Sheet2!$C$3:$C$203,Sheet2!E$3:E$203)","v":{"v":0.5347860007439358,"d":"0.535"}}]
[null,null,"xMax =",1,{"$f":"IF(b>a0/b0,\"Must be smaller than \"&TEXT(a0/b0,\"0.00\"),\"\")","v":""}]
[]
[null,"This corresponds to:",{"$nulls":13},"The area  under the transformed graph"]
[null,null,"q Min  =",{"$f":"theta0","v":{"v":-0.7297276562269663,"d":"-0.730"}},"radians",{"$nulls":10},"from q =",{"$f":"theta0","v":{"v":-0.7297276562269663,"d":"-0.730"}},"to q =",{"$f":"th0","v":{"v":0.33277459985167746,"d":"0.333"}}]
[null,null,"q Max  =",{"$f":"theta00","v":{"v":0.7297276562269663,"d":"0.730"}},"radians",{"$nulls":11},"is about",{"$f":"LOOKUP(ATAN(b0/a0*x0)+0.001,Sheet2!F3:F203,Sheet2!H3:H203)","v":{"v":0.5242143779103192,"d":"0.524"}}]
[]
[]
["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"]
[]
[{"$nulls":8},"          The area  =",null,{"$f":"LOOKUP(x0+dx/2,Sheet2!$C$3:$C$203,Sheet2!F3:F203)","v":{"v":0.33983690945412265,"d":"0.340"}}]
["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."]

{"sheet":"Tangent","index":1,"n_rows":43,"n_cols":19,"rows_kept":43}
[null,"             Visualizing Trig Substitutions"]
[]
[null,null,"    This DIGMath spreadsheet lets you"]
[null,null,"               visualize the process of"]
[null,null,"      Integration with Trig Substitutions"]
[null,null,"              for a function of the form:"]
[]
[]
[]
[]
["What is the value of the constant a?",null,null,3]
[]
["What is the value of the constant b?",null,null,2]
[{"$nulls":9},"Pick a tracing point x0 =",null,null,{"$f":"aa+K15*dxx","v":1}]
["              Your substitution is then x = ",null,null,{"$f":"TEXT(a00/b00,\"0.00\")","v":"1.50"},"tan q",{"$nulls":5},150]
[null,null,"          so that   dx  =",{"$f":"TEXT(a00/b00,\"0.00\")","v":"1.50"},"sec2q dq"]
[{"$nulls":9},"The corresponding transformed point is ",{"$nulls":5},{"$f":"LOOKUP(x00,Sheet2!S3:S203,Sheet2!V3:V203)","v":0.5787149449132},"= q"]
["What is the interval for x for display?  ",null,null,{"$f":"\"  It must be within \"&TEXT(-1.3*a00/b00,\"0.00\")& \" to \"&TEXT(1.3*a00/b00,\"0.00\")","v":"  It must be within -1.95 to 1.95"}]
[null,null,"xMin =",-2,{"$f":"IF(aa<-1.3*a00/b00,\"Must be larger than \"&TEXT(-1.3*a00/b00,\"0.00\"),\"\")","v":"Must be larger than -1.95"},{"$nulls":4}," The area from x =",null,{"$f":"aa","v":-2},"to x =",{"$f":"x00","v":1},"is",{"$f":"LOOKUP(x00+dxx/2,Sheet2!$S$3:$S$203,Sheet2!U$3:U$203)","v":{"v":0.8618737249853202,"d":"0.862"}}]
[null,null,"xMax =",2]
[]
[null,"This corresponds to:",{"$nulls":13},"The area  under the transformed graph"]
[null,null,"q Min  =",{"$f":"ttheta0","v":{"v":-0.9272952180016122,"d":"-0.927"}},"radians",{"$nulls":10},"from q =",{"$f":"ttheta0","v":{"v":-0.9272952180016122,"d":"-0.927"}},"to q =",{"$f":"th00","v":{"v":0.5787149449132,"d":"0.579"}}]
[null,null,"q Max  =",{"$f":"ttheta00","v":{"v":0.9272952180016122,"d":"0.927"}},"radians",{"$nulls":11},"is about",{"$f":"LOOKUP(ATAN(b00/a00*x00)+0.001,Sheet2!V3:V203,Sheet2!X3:X203)","v":{"v":0.8618904233077969,"d":"0.862"}}]
[]
[]
["Click each item below for suggestions and investigations"]
[null,null,"   Item 1"]
[null,null,"   Item 2"]
[null,null,"   Item 3"]
[null,null,"   Item 4"]
[null,null,"   Item 5"]
[]
[{"$nulls":8},"          The area  =",null,{"$f":"LOOKUP(x0+dx/2,Sheet2!$C$3:$C$203,Sheet2!F3:F203)","v":{"v":0.33983690945412265,"d":"0.340"}}]
[]
["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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["dx =",null,-0.9199999999999999,0.42203485949329966,0.0347274748468385,-0.6602740588819114,0.5,0.03472679867252748,null,{"$f":"J9+dx","v":-0.96},0,{"$f":"IF(xx<=x0,L9+dx,L9)","v":-0.96},{"$f":"K11","v":0},{"$f":"IF(xx<=x0,ASIN(b0/a0*xx),N9)","v":-0.6944982656265558},0,null,"dxx =",null,-1.8399999999999999,0.210620153093678,0.03283959693362283,-0.8868451186969318,0.7913139565164876,0.03283973710833319,null,{"$f":"Z9+dxx","v":-1.92},0,{"$f":"IF(xxxx<=x00,AB9+dxx,AB9)","v":-1.92},{"$f":"AA11","v":0},{"$f":"IF(xxxx<=x00,ATAN(b00/a00*xxxx),AD9)","v":-0.9075933340888033},0]
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