And here's what I got back: ๐ต (Big thanks to SlimRunner and Heavenira for the wolfram2desmos script!)
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Expression 13: "C" Subscript, 1 , Baseline left parenthesis, "x" , right parenthesis equals negative "x" co tangent left parenthesis, "a" , right parenthesis plus StartFraction, csc left parenthesis, "a" , right parenthesis cubed left parenthesis, 162 "x" sin left parenthesis, "a" , right parenthesis to the 7th power plus 162 "x" sin left parenthesis, "a" , right parenthesis to the 5th power cos squared left parenthesis, "a" , right parenthesis plus StartRoot, left parenthesis, 162 "x" sin left parenthesis, "a" , right parenthesis to the 7th power plus 162 "x" sin left parenthesis, "a" , right parenthesis to the 5th power cos squared left parenthesis, "a" , right parenthesis , right parenthesis squared plus 4 left parenthesis, 18sin left parenthesis, "a" , right parenthesis cubed cos left parenthesis, "a" , right parenthesis minus 18sin left parenthesis, "a" , right parenthesis to the 4th power , right parenthesis cubed , EndRoot , right parenthesis Superscript, 1 third , Baseline Over 3 left parenthesis, 2 Superscript, 1 third , Baseline , right parenthesis , EndFraction minus StartFraction, 2 Superscript, 1 third , Baseline csc left parenthesis, "a" , right parenthesis cubed left parenthesis, 18sin left parenthesis, "a" , right parenthesis cubed cos left parenthesis, "a" , right parenthesis minus 18sin left parenthesis, "a" , right parenthesis to the 4th power , right parenthesis Over 3 left parenthesis, 162 "x" sin left parenthesis, "a" , right parenthesis to the 7th power plus 162 "x" sin left parenthesis, "a" , right parenthesis to the 5th power cos squared left parenthesis, "a" , right parenthesis plus StartRoot, left parenthesis, 162 "x" sin left parenthesis, "a" , right parenthesis to the 7th power plus 162 "x" sin left parenthesis, "a" , right parenthesis to the 5th power cos squared left parenthesis, "a" , right parenthesis , right parenthesis squared plus 4 left parenthesis, 18sin left parenthesis, "a" , right parenthesis cubed cos left parenthesis, "a" , right parenthesis minus 18sin left parenthesis, "a" , right parenthesis to the 4th power , right parenthesis cubed , EndRoot , right parenthesis Superscript, 1 third , Baseline , EndFraction Has graph. To audio trace, press ALT+T.C1โx=โxcota+csca3162xsina7+162xsina5cos2a+162xsina7+162xsina5cos2a2+418sina3cosaโ18sina4313โ3213โโโ213โcsca318sina3cosaโ18sina43162xsina7+162xsina5cos2a+162xsina7+162xsina5cos2a2+418sina3cosaโ18sina4313โโ
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Not sure how to get the central branch to display as it becomes multivalued. I know it involves the complex results. Perhaps someone can fill me in on that.
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Expression 15: "C" Subscript, 2 , Baseline left parenthesis, "x" , right parenthesis equals negative "x" co tangent left parenthesis, "a" , right parenthesis minus StartFraction, left parenthesis, 1 minus "i" StartRoot, 3 , EndRoot , right parenthesis csc left parenthesis, "a" , right parenthesis cubed left parenthesis, 162 "x" sin left parenthesis, "a" , right parenthesis to the 7th power plus 162 "x" sin left parenthesis, "a" , right parenthesis to the 5th power cos squared left parenthesis, "a" , right parenthesis plus StartRoot, left parenthesis, 162 "x" sin left parenthesis, "a" , right parenthesis to the 7th power plus 162 "x" sin left parenthesis, "a" , right parenthesis to the 5th power cos squared left parenthesis, "a" , right parenthesis , right parenthesis squared plus 4 left parenthesis, 18sin left parenthesis, "a" , right parenthesis cubed cos left parenthesis, "a" , right parenthesis minus 18sin left parenthesis, "a" , right parenthesis to the 4th power , right parenthesis cubed , EndRoot , right parenthesis Superscript, 1 third , Baseline Over 6 left parenthesis, 2 Superscript, 1 third , Baseline , right parenthesis , EndFraction plus StartFraction, left parenthesis, 1 plus "i" StartRoot, 3 , EndRoot , right parenthesis csc left parenthesis, "a" , right parenthesis cubed left parenthesis, 18sin left parenthesis, "a" , right parenthesis cubed cos left parenthesis, "a" , right parenthesis minus 18sin left parenthesis, "a" , right parenthesis to the 4th power , right parenthesis Over 3 times 2 Superscript, 2 thirds , Baseline left parenthesis, 162 "x" sin left parenthesis, "a" , right parenthesis to the 7th power plus 162 "x" sin left parenthesis, "a" , right parenthesis to the 5th power cos squared left parenthesis, "a" , right parenthesis plus StartRoot, left parenthesis, 162 "x" sin left parenthesis, "a" , right parenthesis to the 7th power plus 162 "x" sin left parenthesis, "a" , right parenthesis to the 5th power cos squared left parenthesis, "a" , right parenthesis , right parenthesis squared plus 4 left parenthesis, 18sin left parenthesis, "a" , right parenthesis cubed cos left parenthesis, "a" , right parenthesis minus 18sin left parenthesis, "a" , right parenthesis to the 4th power , right parenthesis cubed , EndRoot , right parenthesis Superscript, 1 third , Baseline , EndFraction Has graph. To audio trace, press ALT+T.C2โx=โxcotaโ1โi3csca3162xsina7+162xsina5cos2a+162xsina7+162xsina5cos2a2+418sina3cosaโ18sina4313โ6213โโ+1+i3csca318sina3cosaโ18sina43ร223โ162xsina7+162xsina5cos2a+162xsina7+162xsina5cos2a2+418sina3cosaโ18sina4313โโ
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Expression 16: "C" Subscript, 3 , Baseline left parenthesis, "x" , right parenthesis equals negative "x" co tangent left parenthesis, "a" , right parenthesis minus StartFraction, left parenthesis, 1 plus "i" StartRoot, 3 , EndRoot , right parenthesis csc left parenthesis, "a" , right parenthesis cubed left parenthesis, 162 "x" sin left parenthesis, "a" , right parenthesis to the 7th power plus 162 "x" sin left parenthesis, "a" , right parenthesis to the 5th power cos squared left parenthesis, "a" , right parenthesis plus StartRoot, left parenthesis, 162 "x" sin left parenthesis, "a" , right parenthesis to the 7th power plus 162 "x" sin left parenthesis, "a" , right parenthesis to the 5th power cos squared left parenthesis, "a" , right parenthesis , right parenthesis squared plus 4 left parenthesis, 18sin left parenthesis, "a" , right parenthesis cubed cos left parenthesis, "a" , right parenthesis minus 18sin left parenthesis, "a" , right parenthesis to the 4th power , right parenthesis cubed , EndRoot , right parenthesis Superscript, 1 third , Baseline Over 6 left parenthesis, 2 Superscript, 1 third , Baseline , right parenthesis , EndFraction plus StartFraction, left parenthesis, 1 minus "i" StartRoot, 3 , EndRoot , right parenthesis csc left parenthesis, "a" , right parenthesis cubed left parenthesis, 18sin left parenthesis, "a" , right parenthesis cubed cos left parenthesis, "a" , right parenthesis minus 18sin left parenthesis, "a" , right parenthesis to the 4th power , right parenthesis Over 3 times 2 Superscript, 2 thirds , Baseline left parenthesis, 162 "x" sin left parenthesis, "a" , right parenthesis to the 7th power plus 162 "x" sin left parenthesis, "a" , right parenthesis to the 5th power cos squared left parenthesis, "a" , right parenthesis plus StartRoot, left parenthesis, 162 "x" sin left parenthesis, "a" , right parenthesis to the 7th power plus 162 "x" sin left parenthesis, "a" , right parenthesis to the 5th power cos squared left parenthesis, "a" , right parenthesis , right parenthesis squared plus 4 left parenthesis, 18sin left parenthesis, "a" , right parenthesis cubed cos left parenthesis, "a" , right parenthesis minus 18sin left parenthesis, "a" , right parenthesis to the 4th power , right parenthesis cubed , EndRoot , right parenthesis Superscript, 1 third , Baseline , EndFraction Has graph. To audio trace, press ALT+T.C3โx=โxcotaโ1+i3csca3162xsina7+162xsina5cos2a+162xsina7+162xsina5cos2a2+418sina3cosaโ18sina4313โ6213โโ+1โi3csca318sina3cosaโ18sina43ร223โ162xsina7+162xsina5cos2a+162xsina7+162xsina5cos2a2+418sina3cosaโ18sina4313โโ