{"text_format":"3","workbook":"xls","n_sheets":1,"sheets":["Sheet1"],"not_rendered":{"images":12,"external_links":4,"defined_names":7},"read":"whole","date_system":"1900","formulas":"cached_only"}

{"sheet":"Sheet1","index":0,"n_rows":187,"n_cols":18,"rows_kept":187,"merged":[[0,3,0,20],[1,3,1,20],[2,3,2,20],[3,5,3,18],[4,5,5,18],[7,4,7,19],[8,4,8,6],[8,7,8,12],[8,13,8,18],[9,4,9,6],[9,7,9,12],[9,13,9,18],[10,4,10,19],[11,4,11,19],[12,5,12,19],[13,5,13,18],[14,4,14,19],[15,4,15,6],[15,7,15,12],[15,13,15,18],[16,4,16,6],[16,7,16,12],[16,13,16,18],[17,4,17,19],[18,4,18,19],[20,5,20,18],[21,5,21,18],[23,4,23,19],[24,4,24,6],[24,8,24,18],[25,4,25,19],[26,4,26,19],[27,4,27,19],[29,17,29,19],[30,6,36,6],[30,7,30,19],[33,7,33,9],[33,10,33,19],[34,10,34,19],[35,10,35,19],[36,7,36,19],[37,5,37,18],[38,4,38,19],[39,5,39,18],[40,5,40,18],[42,17,42,19],[43,6,49,6],[43,7,43,19],[46,7,46,9],[46,10,46,19],[47,10,47,19],[48,10,48,19],[49,7,49,19],[50,5,50,18],[51,4,51,19],[52,5,52,18],[53,5,53,18],[55,17,55,19],[56,7,56,19],[59,6,59,9],[59,10,59,19],[60,10,60,19],[61,10,61,19],[62,7,62,19],[63,5,63,18],[64,4,64,19],[65,5,65,18],[66,5,66,18],[68,17,68,19],[69,6,69,19],[72,7,72,9],[72,10,72,19],[73,10,73,19],[74,10,74,19],[75,6,75,19],[76,5,76,18],[77,4,77,19],[78,5,78,18],[79,5,79,18],[81,17,81,19],[82,5,82,19],[85,5,85,10],[85,11,85,19],[86,5,87,5],[86,10,86,19],[87,10,87,19],[88,5,88,19],[89,5,89,18],[90,4,90,19],[91,5,91,18],[92,5,92,18],[94,17,94,19],[95,6,95,19],[98,5,98,10],[98,11,98,19],[99,10,99,19],[100,10,100,19],[101,6,101,19],[102,5,102,18],[103,4,103,19],[104,5,104,18],[105,5,105,18],[107,17,107,19],[108,6,108,19],[111,5,111,10],[111,11,111,19],[112,10,112,19],[113,10,113,19],[114,6,114,19],[115,5,115,18],[116,4,116,19],[117,5,117,18],[118,5,118,18],[120,17,120,19],[121,6,121,19],[124,6,124,10],[124,11,124,19],[125,10,125,19],[126,10,126,19],[127,6,127,19],[128,5,128,18],[129,4,129,19],[130,5,130,18],[131,5,131,18],[133,17,133,19],[134,6,139,6],[134,7,134,19],[137,7,137,9],[137,10,137,19],[138,10,138,19],[139,10,139,19],[140,7,140,19],[141,5,141,18],[142,4,142,19],[143,5,143,18],[144,5,144,18],[146,17,146,19],[147,6,152,6],[147,7,147,19],[150,7,150,9],[150,10,150,19],[151,10,151,19],[152,10,152,19],[153,7,153,19],[154,5,154,18],[155,4,155,19],[156,5,156,18],[157,5,157,18],[159,17,159,19],[160,7,160,19],[163,6,163,9],[163,10,163,19],[164,10,164,19],[165,10,165,19],[166,7,166,19],[167,5,167,18],[168,4,168,19],[169,5,169,18],[170,5,170,18],[172,17,172,19],[173,6,178,6],[173,7,173,19],[176,7,176,9],[176,10,176,19],[177,10,177,19],[178,10,178,19],[179,7,179,19],[180,5,180,18],[181,4,181,19],[182,5,182,18],[183,5,183,18]],"flags":["formulas_cached_only"]}
[{"$nulls":3},"Tangent-Cotangent-Integral-Calculus-Generator"]
[{"$nulls":3},"Designed to Help Students Practice Solving Trigonometric Integrals"]
[{"$nulls":3},"Created by David Alderoty © 2011, e-mail David@TechForText.com"]
[{"$nulls":5},"     Enter numbers for angles B and A in the white boxes below, and then this software will generate twelve integrals for you to solve, involving tangent and cotangent.  It is best to enter angles less than 90 degrees, but greater than 0 degrees. If this is not done, some of the integrals will not have calculated results."]
[{"$nulls":5},"      You can enter the angles, in either radians or degrees, but if you do not want to deal with decimals enter the angles in degrees.  If you want to enter radians, use the white boxes on the left, but if you want to enter degrees use the boxes on the right.  When numbers are entered in radians, this software was designed to calculate it in terms of a fraction or multiple of PI.  Examples are: if you enter 2, the software calculates it as 2pi radians (=360°), if you enter 1 it is calculated as 1pi (=180°), if you enter 0.5 it is calculated as 0.5pi, (=90°) etc."]
[]
[]
[{"$nulls":4},"INPUT BOX FOR ANGLE B"]
[{"$nulls":4},"Angle",null,null,"INPUT BOX FOR RADIANS, (in terms of a fraction or multiple of pi )",{"$nulls":5},"THIS INPUT BOX IS FOR DEGREES ONLY"]
[null,0,null,null,"  B  ="]
[{"$nulls":4},"The entered angle is 0pi Radians"]
[{"$nulls":4},"This is equal to 0 Degrees"]
[{"$nulls":5},0]
[{"$nulls":5},0]
[{"$nulls":4},"INPUT BOX FOR ANGLE A"]
[{"$nulls":4},"Angle",null,null,"INPUT BOX FOR RADIANS, (in terms of a fraction or multiple of pi )",{"$nulls":5},"THIS INPUT BOX IS FOR DEGREES ONLY"]
[null,0,null,null,"  A  ="]
[{"$nulls":4},"The entered angle is 0pi Radians"]
[{"$nulls":4},"This is equal to 0 Degrees"]
[]
[{"$nulls":5},0]
[{"$nulls":5},0]
[]
[{"$nulls":4},"All the numbers that are calculated by this software are automatically  "]
[{"$nulls":4},"rounded to",null,null,5,"decimal places.  You can change this, by deleting "]
[{"$nulls":4},"the 5 (in blue type) in the above input box.  Then enter the"]
[{"$nulls":4},"number of decimal places you prefer, in the same input box."]
[]
[]
[{"$nulls":17},"Problem 1"]
[{"$nulls":7},"0pi Radians or 0 Degrees"]
[]
[]
[{"$nulls":7},"tan(Q)dQ =",null,null,"The calculated result is concealed"]
[{"$nulls":10},"To display the calculated result, use"]
[{"$nulls":10},"the pink pull-down menu below."]
[{"$nulls":7},"0pi Radians or 0 Degrees"]
[{"$nulls":5},"To display result, left click HERE, and on RED CROSS, and move menu downward"]
[{"$nulls":4},""]
[{"$nulls":5},"Formula Spreadsheet=(-LN(COS(B)))-(-LN(COS(A)))"]
[{"$nulls":5},0]
[]
[{"$nulls":17},"Problem 2"]
[{"$nulls":7},"0pi Radians or 0 Degrees"]
[]
[]
[{"$nulls":7},"cot(Q)dQ =",null,null,"The calculated result is concealed"]
[{"$nulls":10},"To display the calculated result, use"]
[{"$nulls":10},"the pink pull-down menu below."]
[{"$nulls":7},"0pi Radians or 0 Degrees"]
[{"$nulls":5},"To display result, left click HERE, and on RED CROSS, and move menu downward"]
[{"$nulls":4},""]
[{"$nulls":5},"Spreadsheet formula for the above=LN(SIN(B))-LN(SIN(A))"]
[{"$nulls":5},{"$error":"#NUM!"}]
[]
[{"$nulls":17},"Problem 3"]
[{"$nulls":7},"0pi Radians or 0 Degrees"]
[]
[]
[{"$nulls":6},"tan(Q)2dQ =",{"$nulls":3},"The calculated result is concealed"]
[{"$nulls":10},"To display the calculated result, use"]
[{"$nulls":10},"the pink pull-down menu below."]
[{"$nulls":7},"0pi Radians or 0 Degrees"]
[{"$nulls":5},"To display result, left click HERE, and on RED CROSS, and move menu downward"]
[{"$nulls":4},""]
[{"$nulls":5},"Spreadsheet formula=(TAN(B)-B)-(TAN(A)-A)"]
[{"$nulls":5},0]
[]
[{"$nulls":17},"Problem 4"]
[{"$nulls":6},"0pi Radians or 0 Degrees"]
[]
[]
[{"$nulls":7},"cot(Q)2dQ=",null,null,"The calculated result is concealed"]
[{"$nulls":10},"To display the calculated result, use"]
[{"$nulls":10},"the pink pull-down menu below."]
[{"$nulls":6},"  0pi Radians or 0 Degrees"]
[{"$nulls":5},"To display result, left click HERE, and on RED CROSS, and move menu downward"]
[{"$nulls":4},""]
[{"$nulls":5},"Spreadsheet formula=(-B-(1/TAN(B) ))-(-A-(1/TAN(A) ))"]
[{"$nulls":5},{"$error":"#DIV/0!"}]
[]
[{"$nulls":17},"Problem 5"]
[{"$nulls":5},"     0pi Radians or 0 Degrees"]
[]
[]
[{"$nulls":5},"  cot(Q)+tan(Q)dQ =",{"$nulls":5},"The calculated result is concealed"]
[{"$nulls":10},"To display the calculated result,use"]
[{"$nulls":10},"the pink pull-down menu below."]
[{"$nulls":5},"     0pi Radians or 0 Degrees"]
[{"$nulls":5},"To display result, left click HERE, and on RED CROSS, and move menu downward"]
[{"$nulls":4},""]
[{"$nulls":5},"Spreadsheet formula=(LN(SIN(B))-LN(COS(B)))-(LN(SIN(A))-LN(COS(A)))"]
[{"$nulls":5},{"$error":"#NUM!"}]
[]
[{"$nulls":17},"Problem 6"]
[{"$nulls":6},"0pi Radians or 0 Degrees"]
[]
[]
[{"$nulls":5},"  cot(Q)2+tan(Q)2dQ =",{"$nulls":5},"The calculated result is concealed"]
[{"$nulls":10},"To display the calculated result,use"]
[{"$nulls":10},"the pink pull-down menu below."]
[{"$nulls":6},"0pi Radians or 0 Degrees"]
[{"$nulls":5},"To display result, left click HERE, and on RED CROSS, and move menu downward"]
[{"$nulls":4},""]
[{"$nulls":5},"St. F =(TAN(B)-(1/TAN(B))-2*B)-(TAN(A)-(1/TAN(A))-2*A)"]
[{"$nulls":5},{"$error":"#DIV/0!"}]
[]
[{"$nulls":17},"Problem 7"]
[{"$nulls":6},"0pi Radians or 0 Degrees"]
[]
[]
[{"$nulls":5},"  cot(Q)3+tan(Q)3dQ = ",{"$nulls":5},"The calculated result is concealed"]
[{"$nulls":10},"To display the calculated result,use"]
[{"$nulls":10},"the pink pull-down menu below."]
[{"$nulls":6},"0pi Radians or 0 Degrees"]
[{"$nulls":5},"To display result, left click HERE, and on RED CROSS, and move menu downward"]
[{"$nulls":4},""]
[{"$nulls":5},"Sf=(((TAN(B)^2)-((1/TAN(B))^2)+2*LN(COS(B))-2*LN(SIN(B)))-((TAN(A)^2)-((1/TAN(A))^2)+2*LN(COS(A))-2*LN(SIN(A))))/2"]
[{"$nulls":5},{"$error":"#DIV/0!"}]
[]
[{"$nulls":17},"Problem 8"]
[{"$nulls":6},"0pi Radians or 0 Degrees"]
[]
[]
[{"$nulls":5}," ","tan(Q)cot(Q)dQ =",{"$nulls":4},"The calculated result is concealed"]
[{"$nulls":10},"To display the calculated result,use"]
[{"$nulls":10},"the pink pull-down menu below."]
[{"$nulls":6},"0pi Radians or 0 Degrees"]
[{"$nulls":5},"To display result, left click HERE, and on RED CROSS, and move menu downward"]
[{"$nulls":4},""]
[{"$nulls":5},"Spreadsheet formula=B-A"]
[{"$nulls":5},0]
[]
[{"$nulls":17},"Problem 9"]
[{"$nulls":7},"0pi Radians or 0 Degrees"]
[]
[]
[{"$nulls":7},"tan(Q)3dQ=",null,null,"The calculated result is concealed"]
[{"$nulls":10},"To display the calculated result,use"]
[{"$nulls":10},"the pink pull-down menu below."]
[{"$nulls":7},"0pi Radians or 0 Degrees"]
[{"$nulls":5},"To display result, left click HERE, and on RED CROSS, and move menu downward"]
[{"$nulls":4},""]
[{"$nulls":5},"S Formula=((TAN(B)^2+ 2*LN(COS(B)))-(TAN(A)^2+ 2*LN(COS(A))))/2"]
[{"$nulls":5},0]
[]
[{"$nulls":17},"Problem 10"]
[{"$nulls":7},"0pi Radians or 0 Degrees"]
[]
[]
[{"$nulls":7},"cot(Q)3dQ =",null,null,"The calculated result is concealed"]
[{"$nulls":10},"To display the calculated result,use"]
[{"$nulls":10},"the pink pull-down menu below."]
[{"$nulls":7},"0pi Radians or 0 Degrees"]
[{"$nulls":5},"To display result, left click HERE, and on RED CROSS, and move menu downward"]
[{"$nulls":4},""]
[{"$nulls":5},"S f =((-((1/TAN(B))^2)-2*LN(SIN(B)))-(-((1/TAN(A))^2)-2*LN(SIN(A))))/2"]
[{"$nulls":5},{"$error":"#DIV/0!"}]
[{"$nulls":5},"Z"]
[{"$nulls":17},"Problem 11"]
[{"$nulls":7},"0pi Radians or 0 Degrees"]
[]
[]
[{"$nulls":6},"tan(Q)4dQ =",{"$nulls":3},"The calculated result is concealed"]
[{"$nulls":10},"To display the calculated result,use"]
[{"$nulls":10},"the pink pull-down menu below."]
[{"$nulls":7},"0pi Radians or 0 Degrees"]
[{"$nulls":5},"To display result, left click HERE, and on RED CROSS, and move menu downward"]
[{"$nulls":4},""]
[{"$nulls":5},"S f=(((TAN(B)^3)-3*TAN(B)+3*B)-((TAN(A)^3)-3*TAN(A)+3*A))/3"]
[{"$nulls":5},0]
[]
[{"$nulls":17},"Problem 12"]
[{"$nulls":7},"0pi Radians or 0 Degrees"]
[]
[]
[{"$nulls":7},"cot(Q)4dQ =",null,null,"The calculated result is concealed"]
[{"$nulls":10},"To display the calculated result, use"]
[{"$nulls":10},"the pink pull-down menu below."]
[{"$nulls":7},"0pi Radians or 0 Degrees"]
[{"$nulls":5},"To display result, left click HERE, and on RED CROSS, and move menu downward"]
[{"$nulls":4},""]
[{"$nulls":5},"Sf=((3*(1/TAN(B))-((1/TAN(B))^3)+3*B)-(3*(1/TAN(A))-((1/TAN(A))^3)+3*A))/3"]
[{"$nulls":5},{"$error":"#DIV/0!"}]
[]
[{"$nulls":11},"To display result, left click HERE, and on RED CROSS, and move menu downward"]
[{"$nulls":11},"The Calculated Result, Displayed Above in Red Type."]