A199429 -id:A199429 - cp's OEIS frontend

A200338 Decimal expansion of least x > 0 satisfying x^2 + 1 = tan(x).

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

Offset: 1

Clark Kimberling, Nov 16 2011

For many choices of a,b,c, there is exactly one x satisfying a*x^2 + b*x + c = tan(x) and 0 < x < Pi/2.
Guide to related sequences, with graphs included in Mathematica programs:
a.... b.... c.... x
... 0.... 1.... A200338
... 0.... 2.... A200339
... 0.... 3.... A200340
... 0.... 4.... A200341
... 1.... 1.... A200342
... 1.... 2.... A200343
... 1.... 3.... A200344
... 1.... 4.... A200345
... 2.... 1.... A200346
... 2.... 2.... A200347
... 2.... 3.... A200348
... 2.... 4.... A200349
... 3.... 1.... A200350
... 3.... 2.... A200351
... 3.... 3.... A200352
... 3.... 4.... A200353
... 4.... 1.... A200354
... 4.... 2.... A200355
... 4.... 3.... A200356
... 4.... 4.... A200357
... 0.... 1.... A200358
... 0.... 3.... A200359
... 1.... 1.... A200360
... 1.... 2.... A200361
... 1.... 3.... A200362
... 1.... 4.... A200363
... 2.... 1.... A200364
... 2.... 3.... A200365
... 3.... 1.... A200366
... 3.... 2.... A200367
... 3.... 3.... A200368
... 3.... 4.... A200369
... 4.... 1.... A200382
... 4.... 3.... A200383
... 0.... 1.... A200384
... 0.... 2.... A200385
... 0.... 4.... A200386
... 1.... 1.... A200387
... 1.... 2.... A200388
... 1.... 3.... A200389
... 1.... 4.... A200390
... 2.... 1.... A200391
... 2.... 2.... A200392
... 2.... 3.... A200393
... 2.... 4.... A200394
... 3.... 1.... A200395
... 3.... 2.... A200396
... 3.... 4.... A200397
... 4.... 1.... A200398
... 4.... 2.... A200399
... 4.... 3.... A200400
... 4.... 4.... A200401
... 0.... 1.... A200410
... 0.... 3.... A200411
... 1.... 1.... A200412
... 1.... 2.... A200413
... 1.... 3.... A200414
... 1.... 4.... A200415
... 2.... 1.... A200416
... 2.... 3.... A200417
... 3.... 1.... A200418
... 3.... 2.... A200419
... 3.... 3.... A200420
... 3.... 4.... A200421
... 4.... 1.... A200422
... 4.... 3.... A200423
.. -1.... 1.... A200477
.. -1.... 2.... A200478
.. -1.... 3.... A200479
.. -1.... 4.... A200480
.. -2.... 1.... A200481
.. -2.... 2.... A200482
.. -2.... 3.... A200483
.. -2.... 4.... A200484
.. -3.... 1.... A200485
.. -3.... 2.... A200486
.. -3.... 3.... A200487
.. -3.... 4.... A200488
.. -4.... 1.... A200489
.. -4.... 2.... A200490
.. -4.... 3.... A200491
.. -4.... 4.... A200492
.. -1.... 1.... A200493
.. -1.... 2.... A200494
.. -1.... 3.... A200495
.. -1.... 4.... A200496
.. -2.... 1.... A200497
.. -2.... 3.... A200498
.. -3.... 1.... A200499
.. -3.... 2.... A200500
.. -3.... 3.... A200501
.. -3.... 4.... A200502
.. -4.... 1.... A200584
.. -4.... 3.... A200585
.. -1.... 2.... A200586
.. -1.... 3.... A200587
.. -1.... 4.... A200588
.. -2.... 1.... A200589
.. -2.... 2.... A200590
.. -2.... 3.... A200591
.. -2.... 4.... A200592
.. -3.... 1.... A200593
.. -3.... 2.... A200594
.. -3.... 4.... A200595
.. -4.... 1.... A200596
.. -4.... 2.... A200597
.. -4.... 3.... A200598
.. -4.... 4.... A200599
.. -1.... 1.... A200600
.. -1.... 2.... A200601
.. -1.... 3.... A200602
.. -1.... 4.... A200603
.. -2.... 1.... A200604
.. -2.... 3.... A200605
.. -3.... 1.... A200606
.. -3.... 2.... A200607
.. -3.... 3.... A200608
.. -3.... 4.... A200609
.. -4.... 1.... A200610
.. -4.... 3.... A200611
Suppose that f(x,u,v) is a function of three real variables and that g(u,v) is a function defined implicitly by f(g(u,v),u,v)=0.  We call the graph of z=g(u,v) an implicit surface of f.
For an example related to A200338, take f(x,u,v) = x^2 + u*x + v - tan(x) and g(u,v) = a nonzero solution x of f(x,u,v)=0. If there is more than one nonzero solution, care must be taken to ensure that the resulting function g(u,v) is single-valued and continuous.  A portion of an implicit surface is plotted by Program 2 in the Mathematica section.

			x=1.17209361728566903968781879581089880...

Index entries for transcendental numbers.

Cf. A197737, A198414, A198755, A198866, A199170, A199370, A199429, A199597, A199949.

(* Program 1:  A200338 *)
a = 1; b = 0; c = 1;
f[x_] := a*x^2 + b*x + c; g[x_] := Tan[x]
Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.1, 1.2}, WorkingPrecision -> 110]
RealDigits[r]  (* A200338 *)
(* Program 2: implicit surface of x^2+u*x+v=tan(x) *)
f[{x_, u_, v_}] := x^2 + u*x + v - Tan[x];
t = Table[{u, v, x /. FindRoot[f[{x, u, v}] == 0, {x, 0, 1.57}]}, {u, 0, 5, .1}, {v, 0, 5, .1}];
ListPlot3D[Flatten[t, 1]]  (* for A200388 *)

solve(x=1,1.2,x^2+1-tan(x)) \\ Charles R Greathouse IV, Mar 23 2022

A199597 Decimal expansion of x > 0 satisfying x^2 + x*cos(x) = sin(x).

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Nov 08 2011

For many choices of a,b,c, there is exactly one x>0 satisfying a*x^2+b*x*cos(x)=c*sin(x).
Guide to related sequences, with graphs included in Mathematica programs:
a.... b.... c.... x
... 1.... 2.... A199597
... 1.... 3.... A199598
... 1.... 4.... A199599
... 2.... 1.... A199600
... 2.... 3.... A199601
... 2.... 4.... A199602
... 3.... 0.... A199603, A199604
... 3.... 1.... A199605, A199606
... 3.... 2.... A199607, A199608
... 3.... 3.... A199609, A199610
... 4.... 0.... A199611, A199612
... 4.... 1.... A199613, A199614
... 4.... 2.... A199615, A199616
... 4.... 3.... A199617, A199618
... 4.... 4.... A199619, A199620
... 1.... 0.... A199621
... 1.... 2.... A199622
... 1.... 3.... A199623
... 1.... 4.... A199624
... 2.... 1.... A199625
... 2.... 3.... A199661
... 1.... 0.... A199662
... 1.... 2.... A199663
... 1.... 3.... A199664
... 1.... 4.... A199665
... 2.... 0.... A199666
... 2.... 1.... A199667
... 2.... 3.... A199668
... 2.... 4.... A199669
.. -1.... 0.... A003957
.. -1.... 1.... A199722
.. -1.... 2.... A199721
.. -1.... 3.... A199720
.. -1.... 4.... A199719
.. -2.... 1.... A199726
.. -2.... 2.... A199725
.. -2.... 3.... A199724
.. -2.... 4.... A199723
.. -3.... 1.... A199730
.. -3.... 2.... A199729
.. -3.... 3.... A199728
.. -3.... 4.... A199727
.. -4.... 1.... A199737. A199738
.. -4.... 2.... A199735, A199736
.. -4.... 3.... A199733, A199734
.. -4.... 4.... A199731. A199732
.. -1.... 1.... A199742
.. -1.... 2.... A199741
.. -1.... 3.... A199740
.. -1.... 4.... A199739
.. -2.... 1.... A199776
.. -2.... 3.... A199775
.. -3.... 1.... A199780
.. -3.... 2.... A199779
.. -3.... 3.... A199778
.. -3.... 4.... A199777
.. -4.... 1.... A199782
.. -4.... 3.... A199781
.. -4.... 1.... A199786
.. -4.... 2.... A199785
.. -4.... 3.... A199784
.. -4.... 4.... A199783
.. -3.... 1.... A199789
.. -3.... 2.... A199788
.. -3.... 4.... A199787
.. -2.... 1.... A199793
.. -2.... 2.... A199792
.. -2.... 3.... A199791
.. -2.... 4.... A199790
.. -1.... 1.... A199797
.. -1.... 2.... A199796
.. -1.... 3.... A199795
.. -1.... 4.... A199794
.. -4.... 1.... A199873
.. -4.... 3.... A199872
.. -3.... 1.... A199871
.. -3.... 2.... A199870
.. -3.... 3.... A199869
.. -3.... 4.... A199868
.. -2.... 1.... A199867
.. -2.... 3.... A199866
.. -1.... 1.... A199865
.. -1.... 2.... A199864
.. -1.... 3.... A199863
.. -1.... 4.... A199862
Suppose that f(x,u,v) is a function of three real variables and that g(u,v) is a function defined implicitly by f(g(u,v),u,v)=0.  We call the graph of z=g(u,v) an implicit surface of f.
For an example related to A199597, take f(x,u,v)=x^2+u*x*cos(x)-v*sin(x) and g(u,v) = a nonzero solution x of f(x,u,v)=0.  If there is more than one nonzero solution, care must be taken to ensure that the resulting function g(u,v) is single-valued and continuous.  A portion of an implicit surface is plotted by Program 2 in the Mathematica section.

			1.1881851344514388032178109729076525973...

Index entries for transcendental numbers.

Cf. A199370, A199170, A198866, A198755, A198414, A197737, A199429.

(* Program 1:  A199597 *)
a = 1; b = 1; c = 2;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -Pi, Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.18, 1.19}, WorkingPrecision -> 110]
RealDigits[r]  (* A199597 *)
(* Program 2: impl. surf. x^2+u*x*cos(x)=v*sin(x) *)
f[{x_, u_, v_}] := x^2 + u*x*Cos[x] - v*Sin[x];
t = Table[{u, v, x /. FindRoot[f[{x, u, v}] == 0, {x, .5, 3}]}, {u, 0, 2}, {v, u, 20}];
ListPlot3D[Flatten[t, 1]]  (* for A199597 *)

Edited by Georg Fischer, Aug 03 2021

A199460 Decimal expansion of x > 0 satisfying x = 2*sin(x).

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Nov 07 2011

See A199429 for a guide to related sequences. The Mathematica program includes a graph.
A solution to the functional equation f'(z) = f(z+1)-f(z-1) is f(z) = exp(x*i*z). - Jean-François Alcover, Apr 04 2014
The solution c of s/c = 2, where s = arclength and c = chord length on the unit circle. - Clark Kimberling, Jul 08 2020

			1.895494267033980947144035738093601691751...

Index entries for transcendental numbers.

Cf. A199429.

a = 1; b = -2; c = 0;
f[x_] := a*x^2 + b*x*Sin[x]; g[x_] := c*Cos[x]
Plot[{f[x], g[x]}, {x, -Pi, Pi}, {AxesOrigin -> {0, 0}}]
r = x /.  FindRoot[f[x] == g[x], {x, 1.89, 1.90}, WorkingPrecision -> 110]
RealDigits[r]  (* A199460 greatest of three roots *)

Equals lim_{n->oo} x_n where x_(n+1)=2*sin(x_n). - Christoph B. Kassir, Jun 30 2021

A199430 Decimal expansion of x>0 satisfying x^2+xsin(x)=2cos(x).

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Nov 06 2011

See A199429 for a guide to related sequences. The Mathematica program includes a graph.

			0.84085459171733283454408810849983633271467704422...

Index entries for transcendental numbers.

Cf. A199429.

a = 1; b = 1; c = 2;
f[x_] := a*x^2 + b*x*Sin[x]; g[x_] := c*Cos[x]
Plot[{f[x], g[x]}, {x, -2 Pi, 2 Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .64, .65}, WorkingPrecision -> 110]
RealDigits[r]  (* A199430 *)

A199431 Decimal expansion of x>0 satisfying x^2+xsin(x)=3cos(x).

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Nov 06 2011

See A199429 for a guide to related sequences. The Mathematica program includes a graph.

			0.962179505109327091367262754410851473321791...

Index entries for transcendental numbers.

Cf. A199429.

a = 1; b = 1; c = 3;
f[x_] := a*x^2 + b*x*Sin[x]; g[x_] := c*Cos[x]
Plot[{f[x], g[x]}, {x, -Pi, Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .96, .97}, WorkingPrecision -> 110]
RealDigits[r]  (* A199431 *)

A199432 Decimal expansion of x>0 satisfying x^2+2xsin(x)=cos(x).

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Nov 06 2011

See A199370 for a guide to related sequences. The Mathematica program includes a graph.

			0.5430476244074010379607355901437652956070...

Index entries for transcendental numbers.

Cf. A199429.

a = 1; b = 2; c = 1;
f[x_] := a*x^2 + b*x*Sin[x]; g[x_] := c*Cos[x]
Plot[{f[x], g[x]}, {x, -Pi, Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .54, .55}, WorkingPrecision -> 110]
RealDigits[r]  (* A199432 *)

A199433 Decimal expansion of x>0 satisfying x^2+2xsin(x)=2*cos(x).

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Nov 06 2011

See A199370 for a guide to related sequences. The Mathematica program includes a graph.

			0.7268924078543361944600244295359554167196621...

Index entries for transcendental numbers.

Cf. A199429.

a = 1; b = 2; c = 2;
f[x_] := a*x^2 + b*x*Sin[x]; g[x_] := c*Cos[x]
Plot[{f[x], g[x]}, {x, -Pi, Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .72, .73}, WorkingPrecision -> 110]
RealDigits[r]  (* A199433 *)

A199434 Decimal expansion of x>0 satisfying x^2+2xsin(x)=3*cos(x).

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Nov 06 2011

See A199370 for a guide to related sequences. The Mathematica program includes a graph.

			0.8469975300452455894008106375702286795251786774...

Index entries for transcendental numbers.

Cf. A199429.

a = 1; b = 2; c = 3;
f[x_] := a*x^2 + b*x*Sin[x]; g[x_] := c*Cos[x]
Plot[{f[x], g[x]}, {x, -Pi, Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .84, .85}, WorkingPrecision -> 110]
RealDigits[r]  (* A199434 *)

A199435 Decimal expansion of x>0 satisfying x^2+3xsin(x)=cos(x).

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Nov 06 2011

See A199370 for a guide to related sequences. The Mathematica program includes a graph.

			0.477947554121687356519723345940414530738979582349442...

Index entries for transcendental numbers.

Cf. A199429.

a = 1; b = 3; c = 1;
f[x_] := a*x^2 + b*x*Sin[x]; g[x_] := c*Cos[x]
Plot[{f[x], g[x]}, {x, -Pi, Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .47, .48}, WorkingPrecision -> 110]
RealDigits[r]  (* A199435 *)

A199436 Decimal expansion of x>0 satisfying x^2+3xsin(x)=2*cos(x).

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Nov 06 2011

See A199370 for a guide to related sequences. The Mathematica program includes a graph.

			0.6482210358834324109817303939212785430601907...

Index entries for transcendental numbers.

Cf. A199429.

a = 1; b = 3; c = 2;
f[x_] := a*x^2 + b*x*Sin[x]; g[x_] := c*Cos[x]
Plot[{f[x], g[x]}, {x, -Pi, Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .64, .65}, WorkingPrecision -> 110]
RealDigits[r]   (* A199436 *)

cp's OEIS Frontend

A200338 Decimal expansion of least x > 0 satisfying x^2 + 1 = tan(x).

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A199597 Decimal expansion of x > 0 satisfying x^2 + x*cos(x) = sin(x).

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A199460 Decimal expansion of x > 0 satisfying x = 2*sin(x).

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A199430 Decimal expansion of x>0 satisfying x^2+x*sin(x)=2*cos(x).

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A199431 Decimal expansion of x>0 satisfying x^2+x*sin(x)=3*cos(x).

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A199432 Decimal expansion of x>0 satisfying x^2+2*x*sin(x)=cos(x).

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A199433 Decimal expansion of x>0 satisfying x^2+2*x*sin(x)=2*cos(x).

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A199434 Decimal expansion of x>0 satisfying x^2+2*x*sin(x)=3*cos(x).

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A199430 Decimal expansion of x>0 satisfying x^2+xsin(x)=2cos(x).

A199431 Decimal expansion of x>0 satisfying x^2+xsin(x)=3cos(x).

A199432 Decimal expansion of x>0 satisfying x^2+2xsin(x)=cos(x).

A199433 Decimal expansion of x>0 satisfying x^2+2xsin(x)=2*cos(x).

A199434 Decimal expansion of x>0 satisfying x^2+2xsin(x)=3*cos(x).

A199435 Decimal expansion of x>0 satisfying x^2+3xsin(x)=cos(x).

A199436 Decimal expansion of x>0 satisfying x^2+3xsin(x)=2*cos(x).