The OEIS is supported by the many generous donors to the OEIS Foundation.

Decimal expansion of x>0 satisfying x^2-x*cos(x)=3*sin(x).

2

`%I #5 Mar 30 2012 18:57:58
`

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

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

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

`%N Decimal expansion of x>0 satisfying x^2-x*cos(x)=3*sin(x).
`

`%C See A199597 for a guide to related sequences. The Mathematica program includes a graph.
`

`%e x=1.67571335817701527040543489152930460297170170...
`

`%t a = 1; b = -1; c = 3;
`

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

`%t Plot[{f[x], g[x]}, {x, -Pi, Pi}, {AxesOrigin -> {0, 0}}]
`

`%t r = x /. FindRoot[f[x] == g[x], {x, 1.6, 1.7}, WorkingPrecision -> 110]
`

`%t RealDigits[r] (* A199720 *)
`

`%Y Cf. A199597.
`

`%K nonn,cons
`

`%O 1,2
`

`%A _Clark Kimberling_, Nov 09 2011
`