A199950 Decimal expansion of greatest x satisfying x^2 + cos(x) = 2*sin(x).

1, 2, 7, 1, 0, 2, 6, 8, 0, 0, 8, 1, 5, 9, 4, 6, 0, 6, 4, 0, 0, 4, 7, 1, 8, 8, 4, 8, 0, 9, 7, 8, 5, 0, 2, 6, 8, 3, 5, 6, 7, 1, 1, 8, 3, 7, 6, 7, 9, 9, 9, 2, 6, 8, 7, 3, 8, 7, 9, 6, 8, 1, 1, 5, 1, 0, 2, 3, 1, 8, 6, 7, 8, 7, 9, 3, 0, 1, 8, 4, 4, 1, 3, 4, 8, 9, 7, 8, 1, 8, 9, 6, 1, 6, 3, 0, 1, 2, 9

Offset

1,2

Comments

See A199949 for a guide to related sequences. The Mathematica program includes a graph.

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Example

least x:  0.659266045766946074537348579563067611...
greatest x: 1.271026800815946064004718848097850268...

Mathematica

a = 1; b = 1; c = 2;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .65, .66}, WorkingPrecision -> 110]
RealDigits[r]   (* A199949 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.27, 1.28}, WorkingPrecision -> 110]
RealDigits[r]   (* A199950 *)

Prog

(PARI) a=1; b=1; c=2; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jul 05 2018

Crossrefs

Cf. A199949.

Sequence in context: A282681 A113651 A021373 * A364873 A011047 A347589

Adjacent sequences: A199947 A199948 A199949 * A199951 A199952 A199953

Keyword

nonn,cons

Author

Clark Kimberling, Nov 12 2011

Status

approved