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

G. C. Greubel, <a href="/A200102/b200102.txt">Table of n, a(n) for n = 1..10000</a>

(PARI) a=1; b=-4; c=2; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 25 2018

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_Clark Kimberling (ck6(AT)evansville.edu), _, Nov 13 2011

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allocated for Clark KimberlingDecimal expansion of greatest x satisfying x^2-4*cos(x)=2*sin(x).

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

1,2

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

least x: -0.91770131583160047517052439095392148771...

greatest x: 1.50407436560390845625770968131259727...

a = 1; b = -4; c = 2;

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, -.92, -.91}, WorkingPrecision -> 110]

RealDigits[r] (* A200101 *)

r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]

RealDigits[r] (* A200102 *)

Cf. A199949.

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nonn,cons

Clark Kimberling (ck6(AT)evansville.edu), Nov 13 2011

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allocated for Clark Kimberling

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