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A200104
Decimal expansion of greatest x satisfying x^2 - 4*cos(x) = 3*sin(x).
3
1, 6, 4, 3, 5, 5, 6, 5, 6, 7, 5, 2, 0, 1, 7, 1, 6, 5, 6, 9, 0, 6, 5, 2, 4, 7, 6, 1, 6, 3, 4, 8, 8, 8, 1, 6, 9, 4, 6, 0, 7, 4, 9, 2, 9, 7, 7, 5, 1, 3, 9, 1, 4, 8, 5, 7, 2, 0, 1, 3, 8, 1, 5, 2, 2, 6, 2, 9, 4, 3, 3, 5, 9, 0, 4, 2, 1, 6, 1, 2, 9, 4, 5, 5, 9, 5, 8, 9, 8, 4, 0, 0, 3, 6, 4, 1, 3, 8, 4
OFFSET
1,2
COMMENTS
See A199949 for a guide to related sequences. The Mathematica program includes a graph.
LINKS
EXAMPLE
least x: -0.79920081689509700594446006923211010...
greatest x: 1.643556567520171656906524761634888...
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, -3, 3}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.8, -.7}, WorkingPrecision -> 110]
RealDigits[r] (* A200103 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.64, 1.65}, WorkingPrecision -> 110]
RealDigits[r] (* A200104 *)
PROG
(PARI) a=1; b=-4; c=3; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 25 2018
CROSSREFS
Cf. A199949.
Sequence in context: A235509 A346696 A224927 * A154747 A217515 A354619
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Nov 13 2011
STATUS
approved