A199949 -id:A199949 - cp's OEIS frontend

A200106 Decimal expansion of greatest x satisfying x^2 - 4cos(x) = 4sin(x).

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

Offset: 1

Clark Kimberling, Nov 13 2011

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

			least x: -0.698933604732903309337989544733567956233...
greatest x: 1.7695688743727017491150784620016277547...

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

Cf. A199949.

a = 1; b = -4; c = 4;
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, -.7, -.6}, WorkingPrecision -> 110]
RealDigits[r]  (* A200105 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.76, 1.77}, WorkingPrecision -> 110]
RealDigits[r]  (* A200106 *)

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

A200107 Decimal expansion of least x satisfying 2*x^2 - cos(x) = sin(x), negated.

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Nov 13 2011

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

			least x: -0.4690323711198093057335493058025105005500...
greatest x: 0.84026351771576789934797349964835579736...

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

Cf. A199949.

a = 2; b = -1; c = 1;
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, -.47, -.46}, WorkingPrecision -> 110]
RealDigits[r]  (* A200107 *)
r = x /. FindRoot[f[x] == g[x], {x, .84, .85}, WorkingPrecision -> 110]
RealDigits[r]  (* A200108 *)

a=2; b=-1; c=1; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 25 2018

A200108 Decimal expansion of greatest x satisfying 2*x^2 - cos(x) = sin(x).

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Nov 13 2011

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

			least x: -0.4690323711198093057335493058025105005500...
greatest x: 0.840263517715767899347973499648355797365...

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

Cf. A199949.

a = 2; b = -1; c = 1;
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, -.47, -.46}, WorkingPrecision -> 110]
RealDigits[r]  (* A200107 *)
r = x /. FindRoot[f[x] == g[x], {x, .84, .85}, WorkingPrecision -> 110]
RealDigits[r]  (* A200108 *)

a=2; b=-1; c=1; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 25 2018

A200109 Decimal expansion of least x satisfying 2x^2 - cos(x) = 2sin(x), negated.

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Nov 13 2011

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

			least x: -0.35236500577732645310286619535999...
greatest x: 1.056698376942878122192408303117...

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

Cf. A199949.

a = 2; b = -1; 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, -.36, -.35}, WorkingPrecision -> 110]
RealDigits[r]  (* A200109 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.05, 1.06}, WorkingPrecision -> 110]
RealDigits[r]  (* A200110 *)

a=2; b=-1; c=2; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 25 2018

A200110 Decimal expansion of greatest x satisfying 2x^2 - cos(x) = 2sin(x).

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Nov 13 2011

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

			least x: -0.35236500577732645310286619535999...
greatest x: 1.0566983769428781221924083031175250...

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

Cf. A199949.

a = 2; b = -1; 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, -.36, -.35}, WorkingPrecision -> 110]
RealDigits[r]  (* A200109 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.05, 1.06}, WorkingPrecision -> 110]
RealDigits[r]  (* A200110 *)

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

A200112 Decimal expansion of greatest x satisfying 2x^2-cos(x) = 3sin(x).

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Nov 13 2011

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

			least x: -0.27418592805983157901293857616592610671...
greatest x: 1.25741142949475925602237309814803895...

G. C. Greubel, Table of n, a(n) for n = 1..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=1.25, 1.26, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 22 2018

A200114 Decimal expansion of least x satisfying 2x^2 - cos(x) = 4sin(x), negated.

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Nov 13 2011

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

			least x: -0.22123471685655084592875161456517915661...
greatest x: 1.431778732687231131820591799700558843...

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

Cf. A199949.

a = 2; b = -1; c = 4;
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, -.23, -.22}, WorkingPrecision -> 110]
RealDigits[r]  (* A200114 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.43, 1.44}, WorkingPrecision -> 110]
RealDigits[r]  (* A200115 *)

a=2; b=-1; c=4; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 29 2018

A200115 Decimal expansion of greatest x satisfying 2x^2 - cos(x) = 4sin(x).

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Nov 13 2011

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

			least x: -0.22123471685655084592875161456517915661...
greatest x: 1.431778732687231131820591799700558843...

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

Cf. A199949.

a = 2; b = -1; c = 4;
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, -.23, -.22}, WorkingPrecision -> 110]
RealDigits[r]  (* A200114 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.43, 1.44}, WorkingPrecision -> 110]
RealDigits[r]  (* A200115 *)

a=2; b=-1; c=4; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 29 2018

A200116 Decimal expansion of least x satisfying 2x^2 - 2cos(x) = sin(x), negated.

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Nov 14 2011

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

			least x: -0.680326414138679296239631620736419...
greatest x: 0.9847126993630673524991380090748...

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

Cf. A199949.

a = 2; b = -2; c = 1;
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, -.69, -.68}, WorkingPrecision -> 110]
RealDigits[r]  (* A200116 *)
r = x /. FindRoot[f[x] == g[x], {x, .98, .99}, WorkingPrecision -> 110]
RealDigits[r]  (* A200117 *)

a=2; b=-2; c=1; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 29 2018

A200117 Decimal expansion of greatest x satisfying 2x^2 - 2cos(x) = sin(x).

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Nov 14 2011

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

			least x: -0.680326414138679296239631620736419...
greatest x: 0.9847126993630673524991380090748...

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

Cf. A199949.

a = 2; b = -2; c = 1;
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, -.69, -.68}, WorkingPrecision -> 110]
RealDigits[r]  (* A200116 *)
r = x /. FindRoot[f[x] == g[x], {x, .98, .99}, WorkingPrecision -> 110]
RealDigits[r]  (* A200117 *)

a=2; b=-2; c=1; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 29 2018

cp's OEIS Frontend

A200106 Decimal expansion of greatest x satisfying x^2 - 4*cos(x) = 4*sin(x).

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A200107 Decimal expansion of least x satisfying 2*x^2 - cos(x) = sin(x), negated.

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A200108 Decimal expansion of greatest x satisfying 2*x^2 - cos(x) = sin(x).

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A200109 Decimal expansion of least x satisfying 2*x^2 - cos(x) = 2*sin(x), negated.

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A200110 Decimal expansion of greatest x satisfying 2*x^2 - cos(x) = 2*sin(x).

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A200112 Decimal expansion of greatest x satisfying 2*x^2-cos(x) = 3*sin(x).

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A200114 Decimal expansion of least x satisfying 2*x^2 - cos(x) = 4*sin(x), negated.

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Mathematica

PARI

A200115 Decimal expansion of greatest x satisfying 2*x^2 - cos(x) = 4*sin(x).

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A200106 Decimal expansion of greatest x satisfying x^2 - 4cos(x) = 4sin(x).

A200109 Decimal expansion of least x satisfying 2x^2 - cos(x) = 2sin(x), negated.

A200110 Decimal expansion of greatest x satisfying 2x^2 - cos(x) = 2sin(x).

A200112 Decimal expansion of greatest x satisfying 2x^2-cos(x) = 3sin(x).

A200114 Decimal expansion of least x satisfying 2x^2 - cos(x) = 4sin(x), negated.

A200115 Decimal expansion of greatest x satisfying 2x^2 - cos(x) = 4sin(x).

A200116 Decimal expansion of least x satisfying 2x^2 - 2cos(x) = sin(x), negated.

A200117 Decimal expansion of greatest x satisfying 2x^2 - 2cos(x) = sin(x).