Expression 8: "x" equals StartFraction, 2arctan left parenthesis, StartNestedFraction, StartRoot, "c" plus 1 , EndRoot tanh left parenthesis, StartNestedFraction, "y" NestedOver 2 , EndNestedFraction , right parenthesis NestedOver StartRoot, "c" minus 1 , EndRoot , EndNestedFraction , right parenthesis Over StartRoot, "c" minus 1 , EndRoot StartRoot, "c" plus 1 , EndRoot , EndFractionx=2arctanc+1tanhy2c−1c−1c+1
8
Modifying the below function until it sufficiently approximates f(x)^-1:
9
Expression 10: "g" left parenthesis, "y" , right parenthesis equals StartFraction, 2arctan left parenthesis, StartNestedFraction, StartRoot, "c" plus 1 , EndRoot tanh left parenthesis, StartNestedFraction, "y" NestedOver 2 , EndNestedFraction , right parenthesis NestedOver StartRoot, "c" minus 1 , EndRoot , EndNestedFraction , right parenthesis Over StartRoot, "c" minus 1 , EndRoot StartRoot, "c" plus 1 , EndRoot , EndFraction plus StartFraction, "y" Over 29 , EndFraction plus "h" left parenthesis, "y" , right parenthesisgy=2arctanc+1tanhy2c−1c−1c+1+y29+hy
10
Expression 11: "k" equals left bracket, 0 , 1 , 2 , ... , 60 times "b" , right bracketk=0,1,2,...,60·b
equals=
00
11
22
33
44
55
66
77
88
99
1010
1111
1212
1313
1414
61 element list
11
Expression 12: "b" equals 1b=1
11
1010
12
Hidden Label: left parenthesis, StartFraction, "k" pi Over 180 "b" , EndFraction , "f" left parenthesis, StartFraction, "k" pi Over 180 "b" , EndFraction , right parenthesis , right parenthesiskπ180b,fkπ180b
Label
equals=
left parenthesis, 0 , 0 , right parenthesis0,0
left parenthesis, 0.0 1 7 4 5 , 0.3 9 8 3 , right parenthesis0.01745,0.3983
left parenthesis, 0.0 3 4 9 1 , 0.7 9 6 7 , right parenthesis0.03491,0.7967
left parenthesis, 0.0 5 2 3 6 , 1.1 9 5 , right parenthesis0.05236,1.195
left parenthesis, 0.0 6 9 8 1 , 1.5 9 4 , right parenthesis0.06981,1.594
left parenthesis, 0.0 8 7 2 7 , 1.9 9 4 , right parenthesis0.08727,1.994
left parenthesis, 0.1 0 4 7 , 2.3 9 4 , right parenthesis0.1047,2.394
left parenthesis, 0.1 2 2 2 , 2.7 9 5 , right parenthesis0.1222,2.795
left parenthesis, 0.1 3 9 6 , 3.1 9 7 , right parenthesis0.1396,3.197
left parenthesis, 0.1 5 7 1 , 3.6 , right parenthesis0.1571,3.6
left parenthesis, 0.1 7 4 5 , 4.0 0 4 , right parenthesis0.1745,4.004
left parenthesis, 0.1 9 2 , 4.4 0 9 , right parenthesis0.192,4.409
left parenthesis, 0.2 0 9 4 , 4.8 1 6 , right parenthesis0.2094,4.816
left parenthesis, 0.2 2 6 9 , 5.2 2 4 , right parenthesis0.2269,5.224
left parenthesis, 0.2 4 4 3 , 5.6 3 4 , right parenthesis0.2443,5.634
61 element list
13
Hidden Label: left parenthesis, "g" left parenthesis, "f" left parenthesis, StartFraction, "k" pi Over 180 "b" , EndFraction , right parenthesis , right parenthesis , "f" left parenthesis, StartFraction, "k" pi Over 180 "b" , EndFraction , right parenthesis , right parenthesisgfkπ180b,fkπ180b
Label
equals=
left parenthesis, 0 , 0 , right parenthesis0,0
left parenthesis, 0.0 2 5 3 , 0.3 9 8 3 , right parenthesis0.0253,0.3983
left parenthesis, 0.0 4 8 3 9 , 0.7 9 6 7 , right parenthesis0.04839,0.7967
left parenthesis, 0.0 6 8 4 3 , 1.1 9 5 , right parenthesis0.06843,1.195
left parenthesis, 0.0 8 5 8 2 , 1.5 9 4 , right parenthesis0.08582,1.594
left parenthesis, 0.1 0 1 4 , 1.9 9 4 , right parenthesis0.1014,1.994
left parenthesis, 0.1 1 6 , 2.3 9 4 , right parenthesis0.116,2.394
left parenthesis, 0.1 3 0 3 , 2.7 9 5 , right parenthesis0.1303,2.795
left parenthesis, 0.1 4 4 8 , 3.1 9 7 , right parenthesis0.1448,3.197
left parenthesis, 0.1 5 9 7 , 3.6 , right parenthesis0.1597,3.6
left parenthesis, 0.1 7 5 3 , 4.0 0 4 , right parenthesis0.1753,4.004
left parenthesis, 0.1 9 1 7 , 4.4 0 9 , right parenthesis0.1917,4.409
left parenthesis, 0.2 0 8 9 , 4.8 1 6 , right parenthesis0.2089,4.816
left parenthesis, 0.2 2 6 9 , 5.2 2 4 , right parenthesis0.2269,5.224
left parenthesis, 0.2 4 5 6 , 5.6 3 4 , right parenthesis0.2456,5.634
61 element list
14
Hidden Label: left parenthesis, "g" left parenthesis, "f" left parenthesis, StartFraction, "k" pi Over 180 "b" , EndFraction , right parenthesis , right parenthesis minus StartFraction, "k" pi Over 180 "b" , EndFraction , "f" left parenthesis, StartFraction, "k" pi Over 180 "b" , EndFraction , right parenthesis , right parenthesisgfkπ180b−kπ180b,fkπ180b
Label
equals=
left parenthesis, 0 , 0 , right parenthesis0,0
left parenthesis, 0.0 0 7 8 4 2 , 0.3 9 8 3 , right parenthesis0.007842,0.3983
left parenthesis, 0.0 1 3 4 8 , 0.7 9 6 7 , right parenthesis0.01348,0.7967
left parenthesis, 0.0 1 6 0 7 , 1.1 9 5 , right parenthesis0.01607,1.195
left parenthesis, 0.0 1 6 , 1.5 9 4 , right parenthesis0.016,1.594
left parenthesis, 0.0 1 4 1 3 , 1.9 9 4 , right parenthesis0.01413,1.994
left parenthesis, 0.0 1 1 2 8 , 2.3 9 4 , right parenthesis0.01128,2.394
left parenthesis, 0.0 0 8 1 2 6 , 2.7 9 5 , right parenthesis0.008126,2.795
left parenthesis, 0.0 0 5 1 2 8 , 3.1 9 7 , right parenthesis0.005128,3.197
left parenthesis, 0.0 0 2 6 0 8 , 3.6 , right parenthesis0.002608,3.6
left parenthesis, 0.0 0 0 7 6 6 6 , 4.0 0 4 , right parenthesis0.0007666,4.004
left parenthesis, negative 0.0 0 0 2 9 0 6 , 4.4 0 9 , right parenthesis−0.0002906,4.409
left parenthesis, negative 0.0 0 0 5 3 1 , 4.8 1 6 , right parenthesis−0.000531,4.816
left parenthesis, 0.0 0 0 0 1 8 0 5 , 5.2 2 4 , right parenthesis0.00001805,5.224
left parenthesis, 0.0 0 1 2 8 , 5.6 3 4 , right parenthesis0.00128,5.634
61 element list
15
Expression 16: Start sum from "n" equals 0 to 60 "b" , end sum, "g" left parenthesis, "f" left parenthesis, StartFraction, "n" pi Over 180 "b" , EndFraction , right parenthesis , right parenthesis60b∑n=0gfnπ180b
