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A199964
Decimal expansion of greatest x satisfying x^2 + 4*cos(x) = 3*sin(x).
3
2, 1, 7, 8, 8, 4, 3, 3, 0, 3, 0, 3, 8, 4, 3, 8, 4, 7, 8, 7, 4, 7, 3, 5, 1, 5, 4, 6, 6, 3, 1, 1, 2, 0, 7, 8, 8, 0, 9, 8, 3, 8, 5, 5, 8, 5, 8, 9, 3, 8, 0, 7, 1, 9, 4, 3, 7, 4, 9, 0, 8, 7, 6, 0, 0, 4, 7, 5, 6, 4, 2, 6, 7, 4, 4, 8, 5, 4, 0, 4, 7, 5, 3, 2, 0, 2, 9, 5, 4, 4, 4, 8, 4, 5, 2, 5, 9, 8, 6
OFFSET
1,1
COMMENTS
See A199949 for a guide to related sequences. The Mathematica program includes a graph.
LINKS
EXAMPLE
least x: 1.2397511548307033226630942987091820...
greatest x: 2.17884330303843847874735154663112...
MATHEMATICA
a = 1; b = 4; c = 3;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 3}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.23, 1.24}, WorkingPrecision -> 110]
RealDigits[r] (* A199963 *)
r = x /. FindRoot[f[x] == g[x], {x, 2.17, 2.18}, WorkingPrecision -> 110]
RealDigits[r] (* A199964 *)
PROG
(PARI) a=1; b=4; c=3; solve(x=2, 3, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 23 2018
CROSSREFS
Cf. A199949.
Sequence in context: A021463 A371268 A371261 * A217107 A320432 A141513
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Nov 12 2011
STATUS
approved