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{"sheet":"Sheet1","index":0,"n_rows":185,"n_cols":17,"rows_kept":185,"merged":[[0,2,0,19],[1,2,1,19],[2,2,2,19],[3,4,4,17],[6,3,6,18],[7,3,7,5],[7,6,7,11],[7,12,7,17],[8,3,8,5],[8,6,8,11],[8,12,8,17],[9,3,9,18],[10,3,10,18],[12,4,12,17],[13,3,13,18],[14,3,14,5],[14,6,14,11],[14,12,14,17],[15,3,15,5],[15,6,15,11],[15,12,15,17],[16,3,16,18],[17,3,17,18],[19,4,19,17],[21,3,21,18],[22,3,22,5],[22,7,22,17],[23,3,23,18],[24,3,24,18],[25,3,25,18],[28,5,34,5],[28,6,28,15],[28,16,28,18],[31,6,31,8],[31,9,31,18],[32,9,32,18],[33,9,33,18],[34,6,34,15],[35,4,35,17],[36,3,36,18],[37,4,37,17],[38,4,38,17],[41,5,47,5],[41,6,41,15],[41,16,41,18],[44,6,44,8],[44,9,44,18],[45,9,45,18],[46,9,46,18],[47,6,47,15],[48,4,48,17],[49,3,49,18],[50,4,50,17],[51,4,51,17],[54,6,54,15],[54,16,54,18],[57,5,57,8],[57,9,57,18],[58,9,58,18],[59,9,59,18],[60,6,60,15],[61,4,61,17],[62,3,62,18],[63,4,63,17],[64,4,64,17],[67,5,67,15],[67,16,67,18],[70,6,70,8],[70,9,70,18],[71,9,71,18],[72,9,72,18],[73,5,73,15],[74,4,74,17],[75,3,75,18],[76,4,76,17],[77,4,77,17],[80,4,80,15],[80,16,80,18],[83,4,83,9],[83,10,83,18],[84,4,85,4],[84,9,84,18],[85,9,85,18],[86,4,86,15],[87,4,87,17],[88,3,88,18],[89,4,89,17],[90,4,90,17],[93,5,93,15],[93,16,93,18],[96,4,96,9],[96,10,96,18],[97,9,97,18],[98,9,98,18],[99,5,99,15],[100,4,100,17],[101,3,101,18],[102,4,102,17],[103,4,103,17],[106,5,106,15],[106,16,106,18],[109,4,109,9],[109,10,109,18],[110,9,110,18],[111,9,111,18],[112,5,112,15],[113,4,113,17],[114,3,114,18],[115,4,115,17],[116,4,116,17],[119,5,119,15],[119,16,119,18],[122,5,122,9],[122,10,122,18],[123,9,123,18],[124,9,124,18],[125,5,125,15],[126,4,126,17],[127,3,127,18],[128,4,128,17],[129,4,129,17],[132,5,137,5],[132,6,132,15],[132,16,132,18],[135,6,135,8],[135,9,135,18],[136,9,136,18],[137,9,137,18],[138,6,138,15],[139,4,139,17],[140,3,140,18],[141,4,141,17],[142,4,142,17],[145,5,150,5],[145,6,145,15],[145,16,145,18],[148,6,148,8],[148,9,148,18],[149,9,149,18],[150,9,150,18],[151,6,151,15],[152,4,152,17],[153,3,153,18],[154,4,154,17],[155,4,155,17],[158,6,158,15],[158,16,158,18],[161,5,161,8],[161,9,161,18],[162,9,162,18],[163,9,163,18],[164,6,164,15],[165,4,165,17],[166,3,166,18],[167,4,167,17],[168,4,168,17],[171,5,176,5],[171,6,171,15],[171,16,171,18],[174,6,174,8],[174,9,174,18],[175,9,175,18],[176,9,176,18],[177,6,177,15],[178,4,178,17],[179,3,179,18],[180,4,180,17],[181,4,181,17]]}
[null,null,"Trig-Integral-Calculus-Generator"]
[null,null,"Designed to Help Students Practice Solving Trigonometric Integrals"]
[null,null,"Created by David Alderoty © 2011, e-mail David@TechForText.com"]
[{"$nulls":4},"Enter numbers for angles B and A in the white boxes below, and this software will generate twelve trigonometric integrals, for you to solve.  You can enter the numbers for the angles, in either radians or degrees.  If you want to enter radians, use the white boxes on the left, but if you want to enter degrees use the boxes on the right.  When numbers are entered in radians, this software was designed to calculate it in terms of a fraction or multiple of PI.  Examples are: if you enter 2, the software calculates it as 2pi radians (=360°), if you enter 1 it is calculated as 1pi (=180°), if you enter 0.5 it is calculated as 0.5pi, (=90°) etc."]
[]
[]
[{"$nulls":3},{"$f":"IF( (COUNTA(G9  )+COUNTA(M9))=2, \"You cannot enter numbers in both the left and right input box.\", \"INPUT BOX FOR ANGLE B\" )","v":"INPUT BOX FOR ANGLE B"}]
[{"$nulls":3},"Angle",null,null,"INPUT BOX FOR RADIANS, (in terms of a fraction or multiple of pi )",{"$nulls":5},"THIS INPUT BOX IS FOR DEGREES ONLY"]
[{"$f":"PI()*E13","v":0},null,null,"  B  ="]
[{"$nulls":3},{"$f":"\"The entered angle is \"& ROUND(E13, Rd )& \"pi Radians\"","v":"The entered angle is 0pi Radians"}]
[{"$nulls":3},{"$f":"\"This is equal to \"& ROUND((180*E13), Rd)&\" Degrees\"","v":"This is equal to 0 Degrees"}]
[]
[{"$nulls":4},{"$f":"IF(COUNTA(M9)=0,G9, RADIANS(M9)/PI())","v":0}]
[{"$nulls":3},{"$f":"IF( (COUNTA(G16  )+COUNTA(M16))=2, \"You cannot enter numbers in both the left and right input box.\", \"INPUT BOX FOR ANGLE A\" )","v":"INPUT BOX FOR ANGLE A"}]
[{"$nulls":3},"Angle",null,null,"INPUT BOX FOR RADIANS, (in terms of a fraction or multiple of pi )",{"$nulls":5},"THIS INPUT BOX IS FOR DEGREES ONLY"]
[{"$f":"PI()*E20","v":0},null,null,"  A  ="]
[{"$nulls":3},{"$f":"\"The entered angle is \"& ROUND(E20,Rd)&\"pi Radians\"","v":"The entered angle is 0pi Radians"}]
[{"$nulls":3},{"$f":"\"This is equal to \"& ROUND((180*E20), Rd) &\" Degrees\"","v":"This is equal to 0 Degrees"}]
[]
[{"$nulls":4},{"$f":"IF(COUNTA(M16)=0,G16, RADIANS(M16)/PI())","v":0}]
[]
[{"$nulls":3},"All the numbers that are calculated by this software are automatically  "]
[{"$nulls":3},"rounded to",null,null,5,"decimal places.  You can change this, by deleting "]
[{"$nulls":3},{"$f":"\"the \" & Rd& \" (in blue type) in the above input box.  Then enter the\"","v":"the 5 (in blue type) in the above input box.  Then enter the"}]
[{"$nulls":3},"number of decimal places you prefer, in the same input box."]
[]
[]
[]
[{"$nulls":6},{"$f":"ROUND((B/PI()), Rd  )& \"pi Radians\"","v":"0pi Radians"},{"$nulls":9},"Problem 1"]
[]
[]
[{"$nulls":6},"sin(Q)dQ =",null,null,{"$f":"(IF(E36=Hide, \"The calculated result is concealed\",  ROUND(E39,Rd )))","v":"The calculated result is concealed"}]
[{"$nulls":9},{"$f":"IF(E36=Hide, \"To display the calculated result, use\", \"\")","v":"To display the calculated result, use"}]
[{"$nulls":9},{"$f":"IF(E36=Hide, \"the pink pull-down menu below.\", \"\")","v":"the pink pull-down menu below."}]
[{"$nulls":6},{"$f":"ROUND( (A/PI()), Rd )& \"pi Radians\"","v":"0pi Radians"}]
[{"$nulls":4},"To display result, left click HERE, and move the menu downward"]
[{"$nulls":3},{"$f":"IF(E36=Hide, \"\", E38)","v":""}]
[{"$nulls":4},"Formula Spreadsheet for the above =COS(A)-COS(B)"]
[{"$nulls":4},{"$f":"COS(A)-COS(B)","v":0}]
[]
[]
[{"$nulls":6},{"$f":"ROUND((B/PI()), Rd  )&\"pi Radians\"","v":"0pi Radians"},{"$nulls":9},"Problem 2"]
[]
[]
[{"$nulls":6},"cos(Q)dQ =",null,null,{"$f":"(IF(E49=Hide, \"The calculated result is concealed\", ROUND(E52, Rd)) )","v":"The calculated result is concealed"}]
[{"$nulls":9},{"$f":"IF(E49=Hide, \"To display the calculated result, use\", \"\")","v":"To display the calculated result, use"}]
[{"$nulls":9},{"$f":"IF(E49=Hide, \"the pink pull-down menu below.\", \"\")","v":"the pink pull-down menu below."}]
[{"$nulls":6},{"$f":"ROUND( (A/PI()), Rd )& \"pi Radians\"","v":"0pi Radians"}]
[{"$nulls":4},"To display result, left click HERE, and move the menu downward"]
[{"$nulls":3},{"$f":"IF(E49=Hide, \"\", E51)","v":""}]
[{"$nulls":4},"Spreadsheet formula for the above =SIN(B)-SIN(A)"]
[{"$nulls":4},{"$f":"SIN(B)-SIN(A)","v":0}]
[]
[]
[{"$nulls":6},{"$f":"ROUND((B/PI()), Rd  )&\"pi Radians\"","v":"0pi Radians"},{"$nulls":9},"Problem 3"]
[]
[]
[{"$nulls":5},"sin(Q)2dQ =",{"$nulls":3},{"$f":"(IF(E62=Hide, \"The calculated result is concealed\",  ROUND(E65,Rd )))","v":"The calculated result is concealed"}]
[{"$nulls":9},{"$f":"IF(E62=Hide, \"To display the calculated result, use\", \"\")","v":"To display the calculated result, use"}]
[{"$nulls":9},{"$f":"IF(E62=Hide, \"the pink pull-down menu below.\", \"\")","v":"the pink pull-down menu below."}]
[{"$nulls":6},{"$f":"ROUND( (A/PI()), Rd )& \"pi Radians\"","v":"0pi Radians"}]
[{"$nulls":4},"To display result, left click HERE, and move the menu downward"]
[{"$nulls":3},{"$f":"IF(E62=Hide, \"\", E64)","v":""}]
[{"$nulls":4},"Spreadsheet formula=((2*B-SIN(2*B) )-(2*A-SIN(2*A) ))/4"]
[{"$nulls":4},{"$f":"((2*B-SIN(2*B) )-(2*A-SIN(2*A) ))/4","v":0}]
[]
[]
[{"$nulls":5},{"$f":"\"   \"&ROUND((B/PI()), Rd  )& \"pi Radians\"","v":"   0pi Radians"},{"$nulls":10},"Problem 4"]
[]
[]
[{"$nulls":6},"cos(Q)2dQ=",null,null,{"$f":"(IF(E75=Hide, \"The calculated result is concealed\", ROUND(E78, Rd )))","v":"The calculated result is concealed"}]
[{"$nulls":9},{"$f":"IF(E75=Hide, \"To display the calculated result, use\", \"\")","v":"To display the calculated result, use"}]
[{"$nulls":9},{"$f":"IF(E75=Hide, \"the pink pull-down menu below.\", \"\")","v":"the pink pull-down menu below."}]
[{"$nulls":5},{"$f":"\"  \"&ROUND( (A/PI()), Rd )& \"pi Radians\"","v":"  0pi Radians"}]
[{"$nulls":4},"To display result, left click HERE, and move the menu downward"]
[{"$nulls":3},{"$f":"IF(E75=Hide, \"\", E77)","v":""}]
[{"$nulls":4},"Spreadsheet formula=((2*B-SIN(2*B))-(2*A-SIN(2*A) ))/4"]
[{"$nulls":4},{"$f":"((2*B+SIN(2*B))-(2*A+SIN(2*A)))/4","v":0}]
[]
[]
[{"$nulls":4},{"$f":"\"     \"&ROUND((B/PI()), Rd  )& \"pi Radians\"","v":"     0pi Radians"},{"$nulls":11},"Problem 5"]
[]
[]
[{"$nulls":4},"  cos(Q)+sin(Q)dQ =",{"$nulls":5},{"$f":"IF(E88=Hide, \"The calculated result is concealed\", ROUND(E91,Rd))","v":"The calculated result is concealed"}]
[{"$nulls":9},{"$f":"IF(E88=Hide, \"To display the calculated result,use\", \"\")","v":"To display the calculated result,use"}]
[{"$nulls":9},{"$f":"IF(E88=Hide, \"the pink pull-down menu below.\", \"\")","v":"the pink pull-down menu below."}]
[{"$nulls":4},{"$f":"\"     \"&ROUND( (A/PI()), Rd )& \"pi Radians\"","v":"     0pi Radians"}]
[{"$nulls":4},"To display result, left click HERE, and move the menu downward"]
[{"$nulls":3},{"$f":"IF(E88=Hide, \"\", E90)","v":""}]
[{"$nulls":4},"Spreadsheet formula=(SIN(B)-COS(B) )-(SIN(A)-COS(A))"]
[{"$nulls":4},{"$f":"(SIN(B)-COS(B) )-(SIN(A)-COS(A))","v":0}]
[]
[]
[{"$nulls":5},{"$f":"ROUND((B/PI()), Rd  )& \"pi Radians\"","v":"0pi Radians"},{"$nulls":10},"Problem 6"]
[]
[]
[{"$nulls":4},"  cos(Q)+sin(Q)2dQ =",{"$nulls":5},{"$f":"(IF(E101=Hide, \"The calculated result is concealed\", ROUND(E104, Rd )))","v":"The calculated result is concealed"}]
[{"$nulls":9},{"$f":"IF(E101=Hide, \"To display the calculated result,use\", \"\")","v":"To display the calculated result,use"}]
[{"$nulls":9},{"$f":"IF(E101=Hide, \"the pink pull-down menu below.\", \"\")","v":"the pink pull-down menu below."}]
[{"$nulls":5},{"$f":"ROUND( (A/PI()), Rd )& \"pi Radians\"","v":"0pi Radians"}]
[{"$nulls":4},"To display result, left click HERE, and move the menu downward"]
[{"$nulls":3},{"$f":"IF(E101=Hide, \"\", E103)","v":""}]
[{"$nulls":4},"St. F =((2*B-SIN(2*B)+4*SIN(B))-(2*A-SIN(2*A)+4*SIN(A)))/4"]
[{"$nulls":4},{"$f":"((2*B-SIN(2*B)+4*SIN(B))-(2*A-SIN(2*A)+4*SIN(A)))/4","v":0}]
[]
[]
[{"$nulls":5},{"$f":"ROUND((B/PI()), Rd  )& \"pi Radians\"","v":"0pi Radians"},{"$nulls":10},"Problem 7"]
[]
[]
[{"$nulls":4},"  cos(Q)2+sin(Q)2dQ = ",{"$nulls":5},{"$f":"(IF(E114=Hide, \"The calculated result is concealed\",  ROUND(E117,Rd)))","v":"The calculated result is concealed"}]
[{"$nulls":9},{"$f":"IF(E114=Hide, \"To display the calculated result,use\", \"\")","v":"To display the calculated result,use"}]
[{"$nulls":9},{"$f":"IF(E114=Hide, \"the pink pull-down menu below.\", \"\")","v":"the pink pull-down menu below."}]
[{"$nulls":5},{"$f":"ROUND( (A/PI()), Rd )& \"pi Radians\"","v":"0pi Radians"}]
[{"$nulls":4},"To display result, left click HERE, and move the menu downward"]
[{"$nulls":3},{"$f":"IF(E114=Hide, \"\", E116)","v":""}]
[{"$nulls":4},"Spreadsheet formula=B-A"]
[{"$nulls":4},{"$f":"B-A","v":0}]
[]
[]
[{"$nulls":5},{"$f":"ROUND((B/PI()), Rd  )& \"pi Radians\"","v":"0pi Radians"},{"$nulls":10},"Problem 8"]
[]
[]
[{"$nulls":4}," ","cos(Q)sin(Q)dQ =",{"$nulls":4},{"$f":"(IF(E127=Hide, \"The calculated result is concealed\", ROUND( E130,Rd) ))","v":"The calculated result is concealed"}]
[{"$nulls":9},{"$f":"IF(E127=Hide, \"To display the calculated result,use\", \"\")","v":"To display the calculated result,use"}]
[{"$nulls":9},{"$f":"IF(E127=Hide, \"the pink pull-down menu below.\", \"\")","v":"the pink pull-down menu below."}]
[{"$nulls":5},{"$f":"ROUND( (A/PI()), Rd )& \"pi Radians\"","v":"0pi Radians"}]
[{"$nulls":4},"To display result, left click HERE, and move the menu downward"]
[{"$nulls":3},{"$f":"IF(E127=Hide, \"\", E129)","v":""}]
[{"$nulls":4},"Spreadsheet formula=((COS(A)^2)-(COS(B)^2))/2"]
[{"$nulls":4},{"$f":"((COS(A)^2)-(COS(B)^2))/2","v":0}]
[]
[]
[{"$nulls":6},{"$f":"ROUND((B/PI()), Rd  )& \"pi Radians\"","v":"0pi Radians"},{"$nulls":9},"Problem 9"]
[]
[]
[{"$nulls":6},"sin(Q)3dQ=",null,null,{"$f":"(IF(E140=Hide, \"The calculated result is concealed\",  ROUND(E143,Rd )))","v":"The calculated result is concealed"}]
[{"$nulls":9},{"$f":"IF(E140=Hide, \"To display the calculated result,use\", \"\")","v":"To display the calculated result,use"}]
[{"$nulls":9},{"$f":"IF(E140=Hide, \"the pink pull-down menu below.\", \"\")","v":"the pink pull-down menu below."}]
[{"$nulls":6},{"$f":"ROUND( (A/PI()), Rd )& \"pi Radians\"","v":"0pi Radians"}]
[{"$nulls":4},"To display result, left click HERE, and move the menu downward"]
[{"$nulls":3},{"$f":"IF(E140=Hide, \"\", E142)","v":""}]
[{"$nulls":4},"S Formula=((COS(3*B)-9*COS(B))-(COS(3*A)-9*COS(A)))/12"]
[{"$nulls":4},{"$f":"((COS(3*B)-9*COS(B))-(COS(3*A)-9*COS(A)))/12","v":0}]
[]
[]
[{"$nulls":6},{"$f":"ROUND((B/PI()), Rd  )& \"pi Radians\"","v":"0pi Radians"},{"$nulls":9},"Problem 10"]
[]
[]
[{"$nulls":6},"cos(Q)3dQ =",null,null,{"$f":"(IF(E153=Hide, \"The calculated result is concealed\",  ROUND(E156, Rd) ))","v":"The calculated result is concealed"}]
[{"$nulls":9},{"$f":"IF(E153=Hide, \"To display the calculated result,use\", \"\")","v":"To display the calculated result,use"}]
[{"$nulls":9},{"$f":"IF(E153=Hide, \"the pink pull-down menu below.\", \"\")","v":"the pink pull-down menu below."}]
[{"$nulls":6},{"$f":"ROUND( (A/PI()), Rd )& \"pi Radians\"","v":"0pi Radians"}]
[{"$nulls":4},"To display result, left click HERE, and move the menu downward"]
[{"$nulls":3},{"$f":"IF(E153=Hide, \"\", E155)","v":""}]
[{"$nulls":4},"Spreadsheet formula=((3*SIN(B)-(SIN(B)^3))-(3*SIN(A)-(SIN(A)^3)))/3"]
[{"$nulls":4},{"$f":"((3*SIN(B)-(SIN(B)^3))-(3*SIN(A)-(SIN(A)^3)))/3","v":0}]
[]
[]
[{"$nulls":6},{"$f":"ROUND((B/PI()), Rd  )& \"pi Radians\"","v":"0pi Radians"},{"$nulls":9},"Problem 11"]
[]
[]
[{"$nulls":5},"sin(Q)4dQ =",{"$nulls":3},{"$f":"(IF(E166=Hide, \"The calculated result is concealed\",  ROUND(E169, Rd) ))","v":"The calculated result is concealed"}]
[{"$nulls":9},{"$f":"IF(E166=Hide, \"To display the calculated result,use\", \"\")","v":"To display the calculated result,use"}]
[{"$nulls":9},{"$f":"IF(E166=Hide, \"the pink pull-down menu below.\", \"\")","v":"the pink pull-down menu below."}]
[{"$nulls":6},{"$f":"ROUND( (A/PI()), Rd )& \"pi Radians\"","v":"0pi Radians"}]
[{"$nulls":4},"To display result, left click HERE, and move the menu downward"]
[{"$nulls":3},{"$f":"IF(E166=Hide, \"\", E168)","v":""}]
[{"$nulls":4},"Spreadsheet formula=((2*(B^3)+3*(B^2))-(2*(A^3)+3*(A^2)))/6\""]
[{"$nulls":4},{"$f":"((6*B-4*COS(B)*(SIN(B)^3)-3*SIN(2*B))-(6*A-4*COS(A)*(SIN(A)^3)-3*SIN(2*A)))/16","v":0}]
[]
[]
[{"$nulls":6},{"$f":"ROUND((B/PI()), Rd  )& \"pi Radians\"","v":"0pi Radians"},{"$nulls":9},"Problem 12"]
[]
[]
[{"$nulls":6},"cos(Q)4dQ =",null,null,{"$f":"(IF(E179=Hide, \"The calculated result is concealed\",  ROUND(E182, Rd )))","v":"The calculated result is concealed"}]
[{"$nulls":9},{"$f":"IF(E179=Hide, \"To display the calculated result, use\", \"\")","v":"To display the calculated result, use"}]
[{"$nulls":9},{"$f":"IF(E179=Hide, \"the pink pull-down menu below.\", \"\")","v":"the pink pull-down menu below."}]
[{"$nulls":6},{"$f":"ROUND( (A/PI()), Rd )& \"pi Radians\"","v":"0pi Radians"}]
[{"$nulls":4},"To display result, left click HERE, and move the menu downward"]
[{"$nulls":3},{"$f":"IF(E179=Hide, \"\", E181)","v":""}]
[{"$nulls":4},"S.F.=((12*B+8*SIN(2*B)+SIN(4*B))-(12*A+8*SIN(2*A)+SIN(4*A)) )/32"]
[{"$nulls":4},{"$f":"((12*B+8*SIN(2*B)+SIN(4*B))-(12*A+8*SIN(2*A)+SIN(4*A)) )/32","v":0}]
[]
[{"$nulls":10},"To display result, left click HERE, and move the menu downward"]
[{"$nulls":10},"The Calculated Result, Displayed Above in Red Type."]