A199949 -id:A199949 - 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

A200297 Decimal expansion of least x satisfying 4x^2-3cos(x)=2*sin(x).

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Nov 15 2011

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

			least x: -0.58847086928685261649979864856036...
greatest x: 0.922697336548314794603906551791...

G. C. Greubel, Table of n, a(n) for n = 0..10000
Index entries for transcendental numbers.

Cf. A199949.

a = 4; b = -3; c = 2;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.59, -.58}, WorkingPrecision -> 110]
RealDigits[r]   (* A200297 *)
r = x /. FindRoot[f[x] == g[x], {x, .92, .93}, WorkingPrecision -> 110]
RealDigits[r]   (* A200298 *)

a=4; b=-3; c=2; solve(x=-.59, -.58, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 22 2018

A200298 Decimal expansion of greatest x satisfying 4x^2-3cos(x)=2*sin(x).

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Nov 15 2011

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

			least x: -0.58847086928685261649979864856036...
greatest x: 0.922697336548314794603906551791...

G. C. Greubel, Table of n, a(n) for n = 0..10000
Index entries for transcendental numbers.

Cf. A199949.

a = 4; b = -3; c = 2;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.59, -.58}, WorkingPrecision -> 110]
RealDigits[r]   (* A200297 *)
r = x /. FindRoot[f[x] == g[x], {x, .92, .93}, WorkingPrecision -> 110]
RealDigits[r]   (* A200298 *)

a=4; b=-3; c=2; solve(x=.92, .93, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 22 2018

A200111 Decimal expansion of least x satisfying 2x^2-cos(x)=3sin(x).

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Nov 13 2011

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

			least x: -0.2741859280598315790129385761659261067...
greatest x: 1.25741142949475925602237309814803895...

G. C. Greubel, Table of n, a(n) for n = 0..10000
Index entries for transcendental numbers.

Cf. A199949.

a = 2; b = -1; c = 3;
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, -.28, -.27}, WorkingPrecision -> 110]
RealDigits[r]  (* A200111 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.25, 1.26}, WorkingPrecision -> 110]
RealDigits[r]  (* A200112 *)

a=2; b=-1; c=3; solve(x=-.28, -.27, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 22 2018

A200231 Decimal expansion of least x satisfying 3x^2-2cos(x)=2*sin(x).

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Nov 14 2011

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

			least x: -0.508066683701868134653059484203509821...
greatest x: 0.9632913766196791046556418296641642...

G. C. Greubel, Table of n, a(n) for n = 0..10000
Index entries for transcendental numbers.

Cf. A199949.

a = 3; b = -2; c = 2;
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, -.51, -.50}, WorkingPrecision -> 110]
RealDigits[r]   (* A200231 *)
r = x /. FindRoot[f[x] == g[x], {x, .96, .97}, WorkingPrecision -> 110]
RealDigits[r]   (* A200232 *)

a=3; b=-2; c=2; solve(x=-.51, -.50, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 22 2018

A199951 Decimal expansion of least x satisfying x^2 + cos(x) = 3*sin(x).

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Nov 12 2011

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

			least x:  0.36356053985895926625732148372284398566895...
greatest x: 1.771792952982026337265923586449094216220...

G. C. Greubel, Table of n, a(n) for n = 0..10000
Index entries for transcendental numbers.

Cf. A199949.

a = 1; b = 1; c = 3;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .36, .37}, WorkingPrecision -> 110]
RealDigits[r]  (* A199951 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.77, 1.78}, WorkingPrecision -> 110]
RealDigits[r]  (* A199952 *)

a=1; b=1; c=3; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 22 2018

A199952 Decimal expansion of greatest x satisfying x^2 + cos(x) = 3*sin(x).

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Nov 12 2011

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

			least x:  0.36356053985895926625732148372284398566895...
greatest x: 1.771792952982026337265923586449094216220...

G. C. Greubel, Table of n, a(n) for n = 1..10000
Index entries for transcendental numbers.

Cf. A199949.

a = 1; b = 1; c = 3;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .36, .37}, WorkingPrecision -> 110]
RealDigits[r]  (* A199951 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.77, 1.78}, WorkingPrecision -> 110]
RealDigits[r]  (* A199952 *)

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

A199953 Decimal expansion of least x satisfying x^2 + cos(x) = 4*sin(x).

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Nov 12 2011

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

			least x:  0.26157393647481130212296420178312116039782...
greatest x: 2.011137342229330846002506540879639388630...

G. C. Greubel, Table of n, a(n) for n = 0..10000
Index entries for transcendental numbers.

Cf. A199949.

a = 1; b = 1; c = 4;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 3}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .26, .27}, WorkingPrecision -> 110]
RealDigits[r]  (* A199953 *)
r = x /. FindRoot[f[x] == g[x], {x, 2.0, 2.1}, WorkingPrecision -> 110]
RealDigits[r]  (* A199954 *)

a=1; b=1; c=4; solve(x=0, .5, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 22 2018

A199954 Decimal expansion of greatest x satisfying x^2+cos(x)=4*sin(x).

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Nov 12 2011

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

			least x:  0.26157393647481130212296420178312116039782...
greatest x: 2.011137342229330846002506540879639388630...

G. C. Greubel, Table of n, a(n) for n = 1..10000
Index entries for transcendental numbers.

Cf. A199949.

a = 1; b = 1; c = 4;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 3}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .26, .27}, WorkingPrecision -> 110]
RealDigits[r]  (* A199953 *)
r = x /. FindRoot[f[x] == g[x], {x, 2.0, 2.1}, WorkingPrecision -> 110]
RealDigits[r]  (* A199954 *)

a=1; b=1; c=4; solve(x=2, 2.1, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 22 2018

A199955 Decimal expansion of least x satisfying x^2+2cos(x)=3sin(x).

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Nov 12 2011

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

			least x:  0.74080336819413223759642692454702162091742...
greatest x: 1.854778410356751774141939581736998761204...

G. C. Greubel, Table of n, a(n) for n = 0..10000
Index entries for transcendental numbers.

Cf. A199949.

a = 1; b = 2; c = 3;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 3}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .74, .75}, WorkingPrecision -> 110]
RealDigits[r]  (* A199955 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.8, 1.9}, WorkingPrecision -> 110]
RealDigits[r]  (* A199956 *)

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

cp's OEIS Frontend

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

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A200297 Decimal expansion of least x satisfying 4*x^2-3*cos(x)=2*sin(x).

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A200298 Decimal expansion of greatest x satisfying 4*x^2-3*cos(x)=2*sin(x).

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A200111 Decimal expansion of least x satisfying 2*x^2-cos(x)=3*sin(x).

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A200231 Decimal expansion of least x satisfying 3*x^2-2*cos(x)=2*sin(x).

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A199951 Decimal expansion of least x satisfying x^2 + cos(x) = 3*sin(x).

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Mathematica

PARI

A199952 Decimal expansion of greatest x satisfying x^2 + cos(x) = 3*sin(x).

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Keywords

Comments

Examples

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Crossrefs

Programs

Mathematica

PARI

A199953 Decimal expansion of least x satisfying x^2 + cos(x) = 4*sin(x).

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A200297 Decimal expansion of least x satisfying 4x^2-3cos(x)=2*sin(x).

A200298 Decimal expansion of greatest x satisfying 4x^2-3cos(x)=2*sin(x).

A200111 Decimal expansion of least x satisfying 2x^2-cos(x)=3sin(x).

A200231 Decimal expansion of least x satisfying 3x^2-2cos(x)=2*sin(x).

A199955 Decimal expansion of least x satisfying x^2+2cos(x)=3sin(x).