login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A200025 Decimal expansion of greatest x satisfying x^2 - 2*cos(x) = 4*sin(x). 3

%I

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

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

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

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

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

%H G. C. Greubel, <a href="/A200025/b200025.txt">Table of n, a(n) for n = 1..10000</a>

%e least x: -0.42352729471869116185741155509692883402...

%e greatest x: 1.8307334532908635992102359547341478845...

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

%t f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]

%t Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, -.43, -.42}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200024 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.83, 1.84}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200025 *)

%o (PARI) a=1; b=-2; c=4; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 24 2018

%Y Cf. A199949.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Nov 13 2011

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 16 05:49 EDT 2019. Contains 328044 sequences. (Running on oeis4.)