A200242 Decimal expansion of greatest x satisfying 3*x^2 - 3*cos(x) = 4*sin(x).

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

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: -0.495594232798110803966694081360666...
greatest x: 1.2559670249437296288542832153976444...

Mathematica

a = 3; b = -3; c = 4;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.50, -.49}, WorkingPrecision -> 110]
RealDigits[r]   (* A200241 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.25, 1.26}, WorkingPrecision -> 110]
RealDigits[r]   (* A200242 *)

Prog

(PARI) a=3; b=-3; c=4; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 22 2018

Crossrefs

Cf. A199949.

Sequence in context: A336257 A284169 A152781 * A062553 A126357 A377809

Adjacent sequences: A200239 A200240 A200241 * A200243 A200244 A200245

Keyword

nonn,cons

Author

Clark Kimberling, Nov 15 2011

Status

approved