A199949 -id:A199949 - cp's OEIS frontend

A200096 Decimal expansion of greatest x satisfying x^2 - 3cos(x) = 3sin(x).

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

Offset: 1

Clark Kimberling, Nov 13 2011

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

			least x:  -0.677119411697943130184179520098917021...
greatest x: 1.6546997822939010711316866818308006354...

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

Cf. A199949.

a = 1; b = -3; 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, -.88, -.67}, WorkingPrecision -> 110]
RealDigits[r]  (* A200095 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.65, 1.66}, WorkingPrecision -> 110]
RealDigits[r]  (* A200096 *)

a=1; b=-3; c=3; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 24 2018

A200097 Decimal expansion of least x satisfying x^2 - 3cos(x) = 4sin(x), negated.

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Nov 13 2011

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

			least x:  -0.576891176962186435752436597718261688130...
greatest x: 1.79646741863500842707885236614949093773...

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

Cf. A199949.

a = 1; b = -3; 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, -.58, -.57}, WorkingPrecision -> 110]
RealDigits[r]  (* A200097 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.79, 1.80}, WorkingPrecision -> 110]
RealDigits[r]  (* A200098 *)

a=1; b=-3; c=4; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 24 2018

A200098 Decimal expansion of greatest x satisfying x^2 - 3cos(x) = 4sin(x).

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Nov 13 2011

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

			least x:  -0.576891176962186435752436597718261688130...
greatest x: 1.79646741863500842707885236614949093773...

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

Cf. A199949.

a = 1; b = -3; 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, -.58, -.57}, WorkingPrecision -> 110]
RealDigits[r]  (* A200097 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.79, 1.80}, WorkingPrecision -> 110]
RealDigits[r]  (* A200098 *)

a=1; b=-3; c=4; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 24 2018

A200099 Decimal expansion of least x satisfying x^2 - 4*cos(x) = sin(x), negated.

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Nov 13 2011

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

			least x:  -1.053352983600153733281110157999...
greatest x: 1.35457555821585784490890770164646...

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

Cf. A199949.

a = 1; b = -4; 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, -1.06, -1.05}, WorkingPrecision -> 110]
RealDigits[r]  (* A200099 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.35, 1.36}, WorkingPrecision -> 110]
RealDigits[r]  (* A200100 *)

a=1; b=-4; c=1; solve(x=-2, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 24 2018

A200100 Decimal expansion of greatest x satisfying x^2 - 4*cos(x) = sin(x).

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Nov 13 2011

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

			least x:  -1.053352983600153733281110157999...
greatest x: 1.35457555821585784490890770164646...

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

Cf. A199949.

a = 1; b = -4; 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, -1.06, -1.05}, WorkingPrecision -> 110]
RealDigits[r]  (* A200099 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.35, 1.36}, WorkingPrecision -> 110]
RealDigits[r]  (* A200100 *)

a=1; b=-4; c=1; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 24 2018

A200101 Decimal expansion of least x satisfying x^2 - 4cos(x) = 2sin(x), negated.

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Nov 13 2011

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

			least x:  -0.91770131583160047517052439095392148771...
greatest x: 1.50407436560390845625770968131259727...

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

Cf. A199949.

a = 1; b = -4; 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, -.92, -.91}, WorkingPrecision -> 110]
RealDigits[r]  (* A200101 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
RealDigits[r]  (* A200102 *)

a=1; b=-4; c=2; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 25 2018

A200102 Decimal expansion of greatest x satisfying x^2 - 4cos(x) = 2sin(x).

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Nov 13 2011

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

			least x:  -0.91770131583160047517052439095392148771...
greatest x: 1.50407436560390845625770968131259727...

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

Cf. A199949.

a = 1; b = -4; 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, -.92, -.91}, WorkingPrecision -> 110]
RealDigits[r]  (* A200101 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
RealDigits[r]  (* A200102 *)

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

A200103 Decimal expansion of least x satisfying x^2 - 4cos(x) = 3sin(x), negated.

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Nov 13 2011

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

			least x:  -0.79920081689509700594446006923211010...
greatest x: 1.643556567520171656906524761634888...

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

Cf. A199949.

a = 1; b = -4; 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, -.8, -.7}, WorkingPrecision -> 110]
RealDigits[r]  (* A200103 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.64, 1.65}, WorkingPrecision -> 110]
RealDigits[r]  (* A200104 *)

a=1; b=-4; c=3; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 25 2018

A200104 Decimal expansion of greatest x satisfying x^2 - 4cos(x) = 3sin(x).

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Nov 13 2011

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

			least x:  -0.79920081689509700594446006923211010...
greatest x: 1.643556567520171656906524761634888...

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

Cf. A199949.

a = 1; b = -4; 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, -.8, -.7}, WorkingPrecision -> 110]
RealDigits[r]  (* A200103 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.64, 1.65}, WorkingPrecision -> 110]
RealDigits[r]  (* A200104 *)

a=1; b=-4; c=3; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 25 2018

A200105 Decimal expansion of least x satisfying x^2 - 4cos(x) = 4sin(x), negated.

Original entry on oeis.org

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

Offset: 0

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

cp's OEIS Frontend

A200096 Decimal expansion of greatest x satisfying x^2 - 3*cos(x) = 3*sin(x).

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A200097 Decimal expansion of least x satisfying x^2 - 3*cos(x) = 4*sin(x), negated.

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A200098 Decimal expansion of greatest x satisfying x^2 - 3*cos(x) = 4*sin(x).

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A200099 Decimal expansion of least x satisfying x^2 - 4*cos(x) = sin(x), negated.

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Mathematica

PARI

A200100 Decimal expansion of greatest x satisfying x^2 - 4*cos(x) = sin(x).

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Comments

Examples

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Programs

Mathematica

PARI

A200101 Decimal expansion of least x satisfying x^2 - 4*cos(x) = 2*sin(x), negated.

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Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

A200102 Decimal expansion of greatest x satisfying x^2 - 4*cos(x) = 2*sin(x).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

A200103 Decimal expansion of least x satisfying x^2 - 4*cos(x) = 3*sin(x), negated.

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A200096 Decimal expansion of greatest x satisfying x^2 - 3cos(x) = 3sin(x).

A200097 Decimal expansion of least x satisfying x^2 - 3cos(x) = 4sin(x), negated.

A200098 Decimal expansion of greatest x satisfying x^2 - 3cos(x) = 4sin(x).

A200101 Decimal expansion of least x satisfying x^2 - 4cos(x) = 2sin(x), negated.

A200102 Decimal expansion of greatest x satisfying x^2 - 4cos(x) = 2sin(x).

A200103 Decimal expansion of least x satisfying x^2 - 4cos(x) = 3sin(x), negated.

A200104 Decimal expansion of greatest x satisfying x^2 - 4cos(x) = 3sin(x).

A200105 Decimal expansion of least x satisfying x^2 - 4cos(x) = 4sin(x), negated.