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A199961
Decimal expansion of least x satisfying x^2 + 3*cos(x) = 4*sin(x).
3
7, 5, 8, 9, 6, 2, 2, 0, 3, 5, 1, 7, 6, 9, 6, 8, 5, 1, 8, 5, 7, 1, 9, 8, 2, 8, 6, 0, 5, 6, 1, 0, 5, 0, 9, 2, 5, 9, 4, 9, 0, 2, 6, 0, 7, 0, 3, 6, 4, 4, 6, 6, 1, 4, 5, 8, 2, 5, 7, 3, 8, 3, 9, 2, 8, 9, 8, 3, 0, 8, 4, 2, 6, 2, 3, 5, 4, 9, 1, 4, 6, 4, 9, 2, 4, 6, 1, 2, 2, 8, 2, 3, 9, 2, 9, 2, 2, 4, 6
OFFSET
0,1
COMMENTS
See A199949 for a guide to related sequences. The Mathematica program includes a graph.
LINKS
EXAMPLE
least x: 0.7589622035176968518571982860561050925949...
greatest x: 2.23580928206456912111526414831701984424...
MATHEMATICA
a = 1; b = 3; c = 4;
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, .75, .76}, WorkingPrecision -> 110]
RealDigits[r] (* A199961 *)
r = x /. FindRoot[f[x] == g[x], {x, 2.2, 2.3}, WorkingPrecision -> 110]
RealDigits[r] (* A199962 *)
PROG
(PARI) a=1; b= 3; c=4; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 23 2018
CROSSREFS
Cf. A199949.
Sequence in context: A115372 A277682 A335864 * A195059 A347352 A339529
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Nov 12 2011
STATUS
approved