{"text_format":"3","workbook":"xlsx","n_sheets":7,"sheets":["Linear","Quad","Cubic","Quartic","Quintic","6th Degree","Calcs"],"not_rendered":{"charts":6,"macros":1,"external_links":1,"defined_names":55,"comments":6},"read":"whole","date_system":"1900"}

{"sheet":"Linear","index":0,"n_rows":33,"n_cols":15,"rows_kept":33}
[null,"Building Linear Approximations"]
[null,"      to the Cosine Function"]
[]
[null,"   This graphing utility lets you try to"]
[null,"  build the best linear approximation"]
[null,"              to the cosine function"]
[{"$nulls":3},"y = cos x"]
[null,null,"centered about x = 0"]
[]
[]
["Enter the interval for x:  "]
[null,null,"xMin =",-1]
[null,null,"xMax =",2]
[]
[]
["In the linear approximation cos x » a0 + b0x "]
[]
["What is the constant coefficient a0  (-1 to 1)?"]
[null,null,200,null,null,{"$f":"(C19-0)/100-1","v":1},null,null,"The largest deviation at 200 evenly spaced points is",{"$nulls":5},{"$f":"MAX(Calcs!E3:E203)","v":1.416146836547138}]
[]
["What is the linear coefficient b0  (-2 to 2)?",{"$nulls":7},"      The sum of the squares of the 200 deviations is",{"$nulls":5},{"$f":"Calcs!F205","v":70.21837720639707}]
[null,null,200,null,null,{"$f":"2*(C22-0)/200-2","v":0}]
[]
["Your linear polynomial is y =",{"$nulls":3},{"$f":"TEXT(aa00,\"0.00\")&\" + \" &TEXT(bb00,\"0.00\")&\"x  \"","v":"1.00 + 0.00x  "}]
[]
[]
[]
[]
["Click each item below for suggestions and investigations"]
[null,null,"   Item 1"]
[null,null,"   Item 2"]
[null,null,"   Item 3"]
[null,null,"   Item 4"]

{"sheet":"Quad","index":1,"n_rows":37,"n_cols":15,"rows_kept":37}
[null,"Building Quadratic Approximations"]
[null,"        to the Cosine Function"]
[]
[null,"   This graphing utility lets you try to"]
[null,"build the best quadratic approximation"]
[null,"              to the cosine function"]
[{"$nulls":3},"y = cos x"]
[null,null,"centered about x = 0"]
[]
[]
["Enter the interval for x:  "]
[null,null,"xMin =",-1]
[null,null,"xMax =",2]
[]
[]
["In the quadratic approximation cos x » a0 + b0x + c0x2"]
[]
["What is the constant coefficient a0  (-1 to 1)?"]
[null,null,200,null,null,{"$f":"(C19-0)/100-1","v":1},null,null,"The largest deviation at 200 evenly spaced points is",{"$nulls":5},{"$f":"MAX(Calcs!L3:L203)","v":0.18385316345285457}]
[]
["What is the linear coefficient b0  (-2 to 2)?",{"$nulls":7},"      The sum of the squares of the 200 deviations is",{"$nulls":5},{"$f":"Calcs!M205","v":0.6156101651798629}]
[null,null,196,null,null,{"$f":"(C22-0)/100-2","v":-0.040000000000000036}]
[]
["What is the quadratic coefficient c0  (-1 to 1)?"]
[null,null,62,null,null,{"$f":"(C25-0)/100-1","v":-0.38}]
[]
["Your quadratic polynomial is y =",{"$nulls":3},{"$f":"TEXT(a0,\"0.00\")&\" +\" &TEXT(b0,\"0.00\")&\"x  + \"&TEXT(c0,\"0.00\")&\"x^2\"","v":"1.00 +-0.04x  + -0.38x^2"}]
[]
[]
[]
[]
["Click each item below for suggestions and investigations"]
[{"$nulls":3},"   Item 1"]
[{"$nulls":3},"   Item 2"]
[{"$nulls":3},"   Item 3"]
[{"$nulls":3},"   Item 4"]
[{"$nulls":3},"   Item 5"]

{"sheet":"Cubic","index":2,"n_rows":40,"n_cols":15,"rows_kept":40}
[null,"  Building Cubic Approximations"]
[null,"        to the Cosine Function"]
[]
[null,"This graphing utility lets you try to"]
[null,"build the best cubic approximation"]
[null,"              to the cosine function"]
[{"$nulls":3},"y = cos x"]
[null,null,"centered about x = 0"]
[]
[]
["Enter the interval for x:  "]
[null,null,"xMin =",-1]
[null,null,"xMax =",2]
[]
[]
["In the cubic approximation cos x » a0 + b0x + c0x2 + d0x3"]
[]
["What is the constant coefficient a0  (-1 to 1)?"]
[null,null,200,null,null,{"$f":"(C19-0)/100-1","v":1},null,null,"The largest deviation at 200 evenly spaced points is",{"$nulls":5},{"$f":"MAX(Calcs!S3:S203)","v":0.2728023058681398}]
[]
["What is the linear coefficient b0  (-2 to 2)?",{"$nulls":7},"      The sum of the squares of the 200 deviations is",{"$nulls":5},{"$f":"Calcs!T205","v":0.9100888747172292}]
[null,null,200,null,null,{"$f":"(C22-0)/100-2","v":{"v":0,"d":"0.00"}}]
[]
["What is the quadratic coefficient c0  (-1 to 1)?"]
[null,null,39,null,null,{"$f":"(C25-0)/100-1","v":-0.61}]
[]
["What is the cubic coefficient d0  (-0.5 to 0.5)?"]
[null,null,124,null,null,{"$f":"(C28+0.5-0)/200-0.5","v":{"v":0.12250000000000005,"d":"0.12"}}]
[]
["Your cubic polynomial is y =",{"$nulls":3},{"$f":"TEXT(a00,\"0.00\")&\" + \"&TEXT(b00,\"0.00\")&\"x + \"&TEXT(c00,\"0.00\")&\"x^2 + \"&TEXT(d00,\"0.00\")&\"x^3\"","v":"1.00 + 0.00x + -0.61x^2 + 0.12x^3"}]
[]
[]
[]
[]
["Click each item below for suggestions and investigations"]
[{"$nulls":3},"   Item 1"]
[{"$nulls":3},"   Item 2"]
[{"$nulls":3},"   Item 3"]
[{"$nulls":3},"   Item 4"]
[{"$nulls":3},"   Item 5"]

{"sheet":"Quartic","index":3,"n_rows":43,"n_cols":15,"rows_kept":43}
[null,"Building Quartic Approximations"]
[null,"        to the Cosine Function"]
[]
[null,"This graphing utility lets you try to"]
[null,"  build the best quartic approximation"]
[null,"              to the cosine function"]
[{"$nulls":3},"y = cos x"]
[null,null,"centered about x = 0"]
[]
[]
["Enter the interval for x:  "]
[null,null,"xMin =",-1]
[null,null,"xMax =",2]
[]
[]
["In the quartic approximation cos x » a0 + b0x + c0x2 + d0x3 + e0x4"]
[]
["What is the constant coefficient a0  (-1 to 1)?"]
[null,null,198,null,null,{"$f":"(C19-0)/100-1","v":0.98},null,null,"The largest deviation at 200 evenly spaced points is",{"$nulls":5},{"$f":"MAX(Calcs!S3:S203)","v":0.2728023058681398}]
[]
["What is the linear coefficient b0  (0 to 2)?",{"$nulls":7},"      The sum of the squares of the 200 deviations is",{"$nulls":5},{"$f":"Calcs!T205","v":0.9100888747172292}]
[null,null,0,null,null,{"$f":"(C22-0)/100","v":{"v":0,"d":"0.00"}}]
[]
["What is the quadratic coefficient c0  (-1 to 1)?"]
[null,null,0,null,null,{"$f":"(C25-0)/100-1","v":-1}]
[]
["What is the cubic coefficient d0  (-0.5 to 0.5)?"]
[null,null,138,null,null,{"$f":"(C28+0.5-0)/200-0.5","v":{"v":0.1925,"d":"0.19"}}]
[]
["What is the quartic coefficient e0  (-0.5 to 0.5)?"]
[null,null,82,null,null,{"$f":"(C31+0.5-0)/200-0.5","v":{"v":-0.08750000000000002,"d":"-0.09"}}]
[]
["Your quartic polynomial is y =",{"$nulls":3},{"$f":"TEXT(a000,\"0.00\")&\" + \"&TEXT(b000,\"0.00\")&\"x + \"&TEXT(c000,\"0.00\")&\"x^2 + \"&TEXT(d000,\"0.00\")&\"x^3 +\"&TEXT(e000,\"0.00\")&\"x^4\"","v":"0.98 + 0.00x + -1.00x^2 + 0.19x^3 +-0.09x^4"}]
[]
[]
[]
[]
["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"]

{"sheet":"Quintic","index":4,"n_rows":46,"n_cols":15,"rows_kept":46}
[null,"Building Quintic Approximations"]
[null,"        to the Cosine Function"]
[]
[null,"   This graphing utility lets you try to"]
[null,"  build the best quintic approximation"]
[null,"              to the cosine function"]
[{"$nulls":3},"y = cos x"]
[null,null,"centered about x = 0"]
[]
[]
["Enter the interval for x:  "]
[null,null,"xMin =",-1]
[null,null,"xMax =",2]
[]
[]
["In the quartic approximation cos x » a0 + b0x + c0x2 + d0x3 + e0x4 + f0x5"]
[]
["What is the constant coefficient a0  (-1 to 1)?"]
[null,null,100,null,null,{"$f":"(C19-0)/100-1","v":0},null,null,"The largest deviation at 200 evenly spaced points is",{"$nulls":5},{"$f":"MAX(Calcs!AF3:AF203)","v":1.6441468365471363}]
[]
["What is the linear coefficient b0  (0 to 2)?",{"$nulls":7},"      The sum of the squares of the 200 deviations is",{"$nulls":5},{"$f":"Calcs!AH205","v":214.11893884139033}]
[null,null,100,null,null,{"$f":"(C22-0)/100","v":{"v":1,"d":"1.00"}}]
[]
["What is the quadratic coefficient c0  (-1 to 1)?"]
[null,null,121,null,null,{"$f":"(C25-0)/100-1","v":0.20999999999999996}]
[]
["What is the cubic coefficient d0  (-0.5 to 0.5)?"]
[null,null,69,null,null,{"$f":"(C28+0.5-0)/200-0.5","v":{"v":-0.15250000000000002,"d":"-0.15"}}]
[]
["What is the quartic coefficient e0  (-0.5 to 0.5)?"]
[null,null,65,null,null,{"$f":"(C31+0.5-0)/200-0.5","v":{"v":-0.1725,"d":"-0.17"}}]
[]
["What is the quintic coefficient f0  (-0.2 to 0.2)?"]
[null,null,137,null,null,{"$f":"(C34)/500-0.2","v":{"v":0.07400000000000001,"d":"0.074"}}]
[]
["Your quintic polynomial is y =",{"$nulls":3},{"$f":"TEXT(a0000,\"0.00\")&\" + \"&TEXT(b0000,\"0.00\")&\"x + \"&TEXT(c0000,\"0.00\")&\"x^2 + \"&TEXT(d0000,\"0.000\")&\"x^3 + \"&TEXT(e0000,\"0.000\")&\"x^4 + \"&TEXT(f0000,\"0.000\")&\"x^5  \"","v":"0.00 + 1.00x + 0.21x^2 + -0.153x^3 + -0.173x^4 + 0.074x^5  "}]
[]
[]
[]
[]
["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"]

{"sheet":"6th Degree","index":5,"n_rows":47,"n_cols":15,"rows_kept":47}
[null,"Building 6th Degree Approximations"]
[null,"        to the Cosine Function"]
[]
[null,"   This graphing utility lets you try to"]
[null,"build the best 6th degree approximation"]
[null,"              to the cosine function"]
[{"$nulls":3},"y = cos x"]
[null,null,"centered about x = 0"]
[]
[]
["Enter the interval for x:  "]
[null,null,"xMin =",-1]
[null,null,"xMax =",2]
[]
[]
["In the 6th degree approximation cos x » a0 + b0x + c0x2 + d0x3 + e0x4 + f0x5 + g0x6"]
[]
["What is the constant coefficient a0  (-1 to 1)?"]
[null,null,100,null,null,{"$f":"(C19-0)/100-1","v":0},null,null,"The largest deviation at 200 evenly spaced points is",{"$nulls":5},{"$f":"MAX(Calcs!AM3:AM203)","v":8.300146836547038}]
[]
["What is the linear coefficient b0  (0 to 2)?",{"$nulls":7},"      The sum of the squares of the 200 deviations is",{"$nulls":5},{"$f":"Calcs!AO205","v":1041.6486145980746}]
[null,null,100,null,null,{"$f":"(C22-0)/100","v":{"v":1,"d":"1.00"}}]
[]
["What is the quadratic coefficient c0  (-1 to 1)?"]
[null,null,121,null,null,{"$f":"(C25-0)/100-1","v":0.20999999999999996}]
[]
["What is the cubic coefficient d0  (-0.5 to 0.5)?"]
[null,null,69,null,null,{"$f":"(C28+0.5-0)/200-0.5","v":{"v":-0.15250000000000002,"d":"-0.15"}}]
[]
["What is the quartic coefficient e0  (-0.5 to 0.5)?"]
[null,null,65,null,null,{"$f":"(C31+0.5-0)/200-0.5","v":{"v":-0.1725,"d":"-0.17"}}]
[]
["What is the quintic coefficient f0  (-0.2 to 0.2)?"]
[null,null,109,null,null,{"$f":"(C34)/500-0.2","v":{"v":0.017999999999999988,"d":"0.018"}}]
[]
["What is the 6th degree coefficient g0  (-0.2 to 0.2)?"]
[null,null,152,null,null,{"$f":"(C37)/500-0.2","v":{"v":0.10399999999999998,"d":"0.104"}}]
[]
["Your 6th degree polynomial is y =",{"$nulls":3},{"$f":"TEXT(a00000,\"0.00\")&\" + \"&TEXT(b0000,\"0.00\")&\"x + \"&TEXT(c00000,\"0.00\")&\"x^2 + \"&TEXT(d00000,\"0.000\")&\"x^3 + \"&TEXT(e00000,\"0.000\")&\"x^4 + \"&TEXT(f00000,\"0.000\")&\"x^5  \"&TEXT(g00000,\"0.000\")&\"x^6  \"","v":"0.00 + 1.00x + 0.21x^2 + -0.153x^3 + -0.173x^4 + 0.018x^5  0.104x^6  "}]
[]
["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"]
[null,null,"   Item 6"]

{"sheet":"Calcs","index":6,"n_rows":205,"n_cols":42,"rows_kept":205}
[null,"Linear",{"$nulls":6},"Quadatic",{"$nulls":6},"Cubic",{"$nulls":6},"Quartic",{"$nulls":6},"Quintic",{"$nulls":6},"6th degree"]
["x","cos x","P1(x)","Difference","ABS","Squares",null,"x","cos x","P2(x)","Difference","ABS","Squares",null,"x","cos x","P3(x)","Difference","ABS","Squares",null,"x","cos x","P4(x)","Difference","ABS","Squares",null,"x","cos x","P5(x)","Difference","ABS","Squares",null,"x","cos x","P6(x)","Difference","ABS","Squares"]
[{"$f":"a","v":-1},{"$f":"COS(A3)","v":{"v":0.5403023058681398,"d":"0.54030"}},{"$f":"aa00+bb00*A3","v":{"v":1,"d":"1.00000"}},{"$f":"C3-B3","v":{"v":0.45969769413186023,"d":"0.45970"}},{"$f":"ABS(D3)","v":{"v":0.45969769413186023,"d":"0.45970"}},{"$f":"D3^2","v":{"v":0.21132196999014932,"d":"0.2113"}},null,{"$f":"a","v":-1},{"$f":"COS(H3)","v":{"v":0.5403023058681398,"d":"0.54030"}},{"$f":"a0+b0*A3+c0*A3^2","v":{"v":0.66,"d":"0.66000"}},{"$f":"J3-I3","v":{"v":0.11969769413186027,"d":"0.11970"}},{"$f":"ABS(K3)","v":{"v":0.11969769413186027,"d":"0.11970"}},{"$f":"K3^2","v":{"v":0.014327537980484376,"d":"0.0143"}},null,{"$f":"aa","v":-1},{"$f":"COS(O3)","v":{"v":0.5403023058681398,"d":"0.54030"}},{"$f":"a00+b00*O3+c00*O3^2+d00*A3^3","v":{"v":0.26749999999999996,"d":"0.26750"}},{"$f":"Q3-P3","v":{"v":-0.2728023058681398,"d":"-0.27280"}},{"$f":"ABS(R3)","v":{"v":0.2728023058681398,"d":"0.27280"}},{"$f":"R3^2","v":{"v":0.0744210980869741,"d":"0.0744"}},null,{"$f":"aaa","v":-1},{"$f":"COS(V3)","v":{"v":0.5403023058681398,"d":"0.54030"}},{"$f":"a000+b000*V3+c000*V3^2+d000*O3^3+e000*O3^4","v":{"v":-0.30000000000000004,"d":"-0.30000"}},{"$f":"X3-W3","v":{"v":-0.8403023058681398,"d":"-0.84030"}},{"$f":"ABS(Y3)","v":{"v":0.8403023058681398,"d":"0.84030"}},{"$f":"Y3^2","v":{"v":0.7061079652473128,"d":"0.7061"}},null,{"$f":"aaaa","v":-1},{"$f":"COS(AC3)","v":{"v":0.5403023058681398,"d":"0.54030"}},{"$f":"a0000+b0000*AC3+c0000*AC3^2+d0000*AC3^3+e0000*AC3^4+f0000*AC3^5","v":{"v":-0.8839999999999999,"d":"-0.88400"}},{"$f":"AE3-AD3","v":{"v":-1.4243023058681397,"d":"-1.42430"}},{"$f":"ABS(AF3)","v":{"v":1.4243023058681397,"d":"1.42430"}},{"$f":"AF3^2","v":{"v":2.0286370585012996,"d":"2.0286"}},null,{"$f":"aaaaa","v":-1},{"$f":"COS(AJ3)","v":{"v":0.5403023058681398,"d":"0.54030"}},{"$f":"a0000+b0000*AJ3+c0000*AJ3^2+d0000*AJ3^3+e0000*AJ3^4+f0000*AJ3^5+g00000*AJ3^6","v":{"v":-0.7799999999999999,"d":"-0.78000"}},{"$f":"AL3-AK3","v":{"v":-1.3203023058681396,"d":"-1.32030"}},{"$f":"ABS(AM3)","v":{"v":1.3203023058681396,"d":"1.32030"}},{"$f":"AM3^2","v":{"v":1.7431981788807265,"d":"1.7432"}}]
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[]
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