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sin2(x)-sin(x)=2cos(x)-1 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
   2                           
sin (x) - sin(x) = 2*cos(x) - 1
$$\sin^{2}{\left(x \right)} - \sin{\left(x \right)} = 2 \cos{\left(x \right)} - 1$$
Gráfica
Respuesta rápida [src]
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           |    |                                                                                         /               /        ______                                                                                                     ||         |    |                                                                                         /               /        ______                                                                                                     ||
           |    |                                                                                        /     22        /  4    \/ 1299                                       2                                                 2            ||         |    |                                                                                        /     22        /  4    \/ 1299                                       2                                                 2            ||
           |    |                                                                                       /    - -- - 2*3 /   -- + --------  - ---------------------------------------------------------------------- + ----------------------- ||         |    |                                                                                       /    - -- - 2*3 /   -- + --------  - ---------------------------------------------------------------------- + ----------------------- ||
           |    |                _________________________________________________________             /       9      \/    27     243                    _________________________________________________________           _______________ ||         |    |                _________________________________________________________             /       9      \/    27     243                    _________________________________________________________           _______________ ||
           |    |               /               _______________                                       /                                                  /               _______________                                     /        ______  ||         |    |               /               _______________                                       /                                                  /               _______________                                     /        ______  ||
           |    |              /               /        ______                                       /                                                  /               /        ______                                     /  4    \/ 1299   ||         |    |              /               /        ______                                       /                                                  /               /        ______                                     /  4    \/ 1299   ||
           |    |             /     11        /  4    \/ 1299                2                      /                                                  /     11        /  4    \/ 1299                2               27*3 /   -- + --------  ||         |    |             /     11        /  4    \/ 1299                2                      /                                                  /     11        /  4    \/ 1299                2               27*3 /   -- + --------  ||
           |    |            /    - -- + 2*3 /   -- + --------  - -----------------------          /                                         27*      /    - -- + 2*3 /   -- + --------  - -----------------------       \/    27     243     ||         |    |            /    - -- + 2*3 /   -- + --------  - -----------------------          /                                         27*      /    - -- + 2*3 /   -- + --------  - -----------------------       \/    27     243     ||
           |    |           /       9      \/    27     243               _______________         /                                                  /       9      \/    27     243               _______________                            ||         |    |           /       9      \/    27     243               _______________         /                                                  /       9      \/    27     243               _______________                            ||
           |    |          /                                             /        ______         /                                                  /                                             /        ______                             ||         |    |          /                                             /        ______         /                                                  /                                             /        ______                             ||
           |    |         /                                             /  4    \/ 1299         /                                                  /                                             /  4    \/ 1299                              ||         |    |         /                                             /  4    \/ 1299         /                                                  /                                             /  4    \/ 1299                              ||
           |    |        /                                        27*3 /   -- + --------       /                                                  /                                        27*3 /   -- + --------                             ||         |    |        /                                        27*3 /   -- + --------       /                                                  /                                        27*3 /   -- + --------                             ||
           |    |  1   \/                                            \/    27     243        \/                                                 \/                                            \/    27     243                                ||         |    |  1   \/                                            \/    27     243        \/                                                 \/                                            \/    27     243                                ||
x1 = - 2*re|atan|- - + ------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------|| - 2*I*im|atan|- - + ------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------||
           \    \  6                                    2                                                                                                            2                                                                        //         \    \  6                                    2                                                                                                            2                                                                        //
$$x_{1} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{1}{6} + \frac{\sqrt{- \frac{11}{9} - \frac{2}{27 \sqrt[3]{\frac{4}{27} + \frac{\sqrt{1299}}{243}}} + 2 \sqrt[3]{\frac{4}{27} + \frac{\sqrt{1299}}{243}}}}{2} + \frac{\sqrt{- \frac{2}{27 \sqrt{- \frac{11}{9} - \frac{2}{27 \sqrt[3]{\frac{4}{27} + \frac{\sqrt{1299}}{243}}} + 2 \sqrt[3]{\frac{4}{27} + \frac{\sqrt{1299}}{243}}}} - \frac{22}{9} - 2 \sqrt[3]{\frac{4}{27} + \frac{\sqrt{1299}}{243}} + \frac{2}{27 \sqrt[3]{\frac{4}{27} + \frac{\sqrt{1299}}{243}}}}}{2} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{1}{6} + \frac{\sqrt{- \frac{11}{9} - \frac{2}{27 \sqrt[3]{\frac{4}{27} + \frac{\sqrt{1299}}{243}}} + 2 \sqrt[3]{\frac{4}{27} + \frac{\sqrt{1299}}{243}}}}{2} + \frac{\sqrt{- \frac{2}{27 \sqrt{- \frac{11}{9} - \frac{2}{27 \sqrt[3]{\frac{4}{27} + \frac{\sqrt{1299}}{243}}} + 2 \sqrt[3]{\frac{4}{27} + \frac{\sqrt{1299}}{243}}}} - \frac{22}{9} - 2 \sqrt[3]{\frac{4}{27} + \frac{\sqrt{1299}}{243}} + \frac{2}{27 \sqrt[3]{\frac{4}{27} + \frac{\sqrt{1299}}{243}}}}}{2} \right)}\right)}$$
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         |    |                 /               /        ______                                                                                                                                                                           ||         |    |                 /               /        ______                                                                                                                                                                           ||
         |    |                /     22        /  4    \/ 1299                                       2                                                 2                                                                                  ||         |    |                /     22        /  4    \/ 1299                                       2                                                 2                                                                                  ||
         |    |               /    - -- - 2*3 /   -- + --------  - ---------------------------------------------------------------------- + -----------------------                                                                       ||         |    |               /    - -- - 2*3 /   -- + --------  - ---------------------------------------------------------------------- + -----------------------                                                                       ||
         |    |              /       9      \/    27     243                    _________________________________________________________           _______________              _________________________________________________________||         |    |              /       9      \/    27     243                    _________________________________________________________           _______________              _________________________________________________________||
         |    |             /                                                  /               _______________                                     /        ______              /               _______________                           ||         |    |             /                                                  /               _______________                                     /        ______              /               _______________                           ||
         |    |            /                                                  /               /        ______                                     /  4    \/ 1299              /               /        ______                            ||         |    |            /                                                  /               /        ______                                     /  4    \/ 1299              /               /        ______                            ||
         |    |           /                                                  /     11        /  4    \/ 1299                2               27*3 /   -- + --------            /     11        /  4    \/ 1299                2            ||         |    |           /                                                  /     11        /  4    \/ 1299                2               27*3 /   -- + --------            /     11        /  4    \/ 1299                2            ||
         |    |          /                                         27*      /    - -- + 2*3 /   -- + --------  - -----------------------       \/    27     243              /    - -- + 2*3 /   -- + --------  - ----------------------- ||         |    |          /                                         27*      /    - -- + 2*3 /   -- + --------  - -----------------------       \/    27     243              /    - -- + 2*3 /   -- + --------  - ----------------------- ||
         |    |         /                                                  /       9      \/    27     243               _______________                                    /       9      \/    27     243               _______________ ||         |    |         /                                                  /       9      \/    27     243               _______________                                    /       9      \/    27     243               _______________ ||
         |    |        /                                                  /                                             /        ______                                    /                                             /        ______  ||         |    |        /                                                  /                                             /        ______                                    /                                             /        ______  ||
         |    |       /                                                  /                                             /  4    \/ 1299                                    /                                             /  4    \/ 1299   ||         |    |       /                                                  /                                             /  4    \/ 1299                                    /                                             /  4    \/ 1299   ||
         |    |      /                                                  /                                        27*3 /   -- + --------                                  /                                        27*3 /   -- + --------  ||         |    |      /                                                  /                                        27*3 /   -- + --------                                  /                                        27*3 /   -- + --------  ||
         |    |1   \/                                                 \/                                            \/    27     243                                   \/                                            \/    27     243     ||         |    |1   \/                                                 \/                                            \/    27     243                                   \/                                            \/    27     243     ||
x2 = 2*re|atan|- + ------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------|| + 2*I*im|atan|- + ------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------||
         \    \6                                                                           2                                                                                                            2                                 //         \    \6                                                                           2                                                                                                            2                                 //
$$x_{2} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{- \frac{11}{9} - \frac{2}{27 \sqrt[3]{\frac{4}{27} + \frac{\sqrt{1299}}{243}}} + 2 \sqrt[3]{\frac{4}{27} + \frac{\sqrt{1299}}{243}}}}{2} + \frac{1}{6} + \frac{\sqrt{- \frac{2}{27 \sqrt{- \frac{11}{9} - \frac{2}{27 \sqrt[3]{\frac{4}{27} + \frac{\sqrt{1299}}{243}}} + 2 \sqrt[3]{\frac{4}{27} + \frac{\sqrt{1299}}{243}}}} - \frac{22}{9} - 2 \sqrt[3]{\frac{4}{27} + \frac{\sqrt{1299}}{243}} + \frac{2}{27 \sqrt[3]{\frac{4}{27} + \frac{\sqrt{1299}}{243}}}}}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{- \frac{11}{9} - \frac{2}{27 \sqrt[3]{\frac{4}{27} + \frac{\sqrt{1299}}{243}}} + 2 \sqrt[3]{\frac{4}{27} + \frac{\sqrt{1299}}{243}}}}{2} + \frac{1}{6} + \frac{\sqrt{- \frac{2}{27 \sqrt{- \frac{11}{9} - \frac{2}{27 \sqrt[3]{\frac{4}{27} + \frac{\sqrt{1299}}{243}}} + 2 \sqrt[3]{\frac{4}{27} + \frac{\sqrt{1299}}{243}}}} - \frac{22}{9} - 2 \sqrt[3]{\frac{4}{27} + \frac{\sqrt{1299}}{243}} + \frac{2}{27 \sqrt[3]{\frac{4}{27} + \frac{\sqrt{1299}}{243}}}}}{2} \right)}\right)}$$
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           |                                                                                      /     22        /  4    \/ 1299                2                                                2                                    |
           |                                                                                     /    - -- - 2*3 /   -- + --------  + ----------------------- + ---------------------------------------------------------------------- |
           |              _________________________________________________________             /       9      \/    27     243               _______________                _________________________________________________________ |
           |             /               _______________                                       /                                             /        ______                /               _______________                            |
           |            /               /        ______                                       /                                             /  4    \/ 1299                /               /        ______                             |
           |           /     11        /  4    \/ 1299                2                      /                                        27*3 /   -- + --------              /     11        /  4    \/ 1299                2             |
           |          /    - -- + 2*3 /   -- + --------  - -----------------------          /                                            \/    27     243       27*      /    - -- + 2*3 /   -- + --------  - -----------------------  |
           |         /       9      \/    27     243               _______________         /                                                                            /       9      \/    27     243               _______________  |
           |        /                                             /        ______         /                                                                            /                                             /        ______   |
           |       /                                             /  4    \/ 1299         /                                                                            /                                             /  4    \/ 1299    |
           |      /                                        27*3 /   -- + --------       /                                                                            /                                        27*3 /   -- + --------   |
           |1   \/                                            \/    27     243        \/                                                                           \/                                            \/    27     243      |
x3 = 2*atan|- + ------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------|
           \6                                    2                                                                                                            2                                                                        /
$$x_{3} = 2 \operatorname{atan}{\left(\frac{\sqrt{- \frac{11}{9} - \frac{2}{27 \sqrt[3]{\frac{4}{27} + \frac{\sqrt{1299}}{243}}} + 2 \sqrt[3]{\frac{4}{27} + \frac{\sqrt{1299}}{243}}}}{2} + \frac{1}{6} + \frac{\sqrt{- \frac{22}{9} - 2 \sqrt[3]{\frac{4}{27} + \frac{\sqrt{1299}}{243}} + \frac{2}{27 \sqrt[3]{\frac{4}{27} + \frac{\sqrt{1299}}{243}}} + \frac{2}{27 \sqrt{- \frac{11}{9} - \frac{2}{27 \sqrt[3]{\frac{4}{27} + \frac{\sqrt{1299}}{243}}} + 2 \sqrt[3]{\frac{4}{27} + \frac{\sqrt{1299}}{243}}}}}}{2} \right)}$$
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           |                                                                                       /               /        ______                                                                                                     |
           |                                                                                      /     22        /  4    \/ 1299                2                                                2                                    |
           |                                                                                     /    - -- - 2*3 /   -- + --------  + ----------------------- + ---------------------------------------------------------------------- |
           |              _________________________________________________________             /       9      \/    27     243               _______________                _________________________________________________________ |
           |             /               _______________                                       /                                             /        ______                /               _______________                            |
           |            /               /        ______                                       /                                             /  4    \/ 1299                /               /        ______                             |
           |           /     11        /  4    \/ 1299                2                      /                                        27*3 /   -- + --------              /     11        /  4    \/ 1299                2             |
           |          /    - -- + 2*3 /   -- + --------  - -----------------------          /                                            \/    27     243       27*      /    - -- + 2*3 /   -- + --------  - -----------------------  |
           |         /       9      \/    27     243               _______________         /                                                                            /       9      \/    27     243               _______________  |
           |        /                                             /        ______         /                                                                            /                                             /        ______   |
           |       /                                             /  4    \/ 1299         /                                                                            /                                             /  4    \/ 1299    |
           |      /                                        27*3 /   -- + --------       /                                                                            /                                        27*3 /   -- + --------   |
           |1   \/                                            \/    27     243        \/                                                                           \/                                            \/    27     243      |
x4 = 2*atan|- + ------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------|
           \6                                    2                                                                                                            2                                                                        /
$$x_{4} = 2 \operatorname{atan}{\left(- \frac{\sqrt{- \frac{22}{9} - 2 \sqrt[3]{\frac{4}{27} + \frac{\sqrt{1299}}{243}} + \frac{2}{27 \sqrt[3]{\frac{4}{27} + \frac{\sqrt{1299}}{243}}} + \frac{2}{27 \sqrt{- \frac{11}{9} - \frac{2}{27 \sqrt[3]{\frac{4}{27} + \frac{\sqrt{1299}}{243}}} + 2 \sqrt[3]{\frac{4}{27} + \frac{\sqrt{1299}}{243}}}}}}{2} + \frac{\sqrt{- \frac{11}{9} - \frac{2}{27 \sqrt[3]{\frac{4}{27} + \frac{\sqrt{1299}}{243}}} + 2 \sqrt[3]{\frac{4}{27} + \frac{\sqrt{1299}}{243}}}}{2} + \frac{1}{6} \right)}$$
x4 = 2*atan(-sqrt(-22/9 - 2*(4/27 + sqrt(1299)/243)^(1/3) + 2/(27*(4/27 + sqrt(1299)/243)^(1/3)) + 2/(27*sqrt(-11/9 - 2/(27*(4/27 + sqrt(1299)/243)^(1/3)) + 2*(4/27 + sqrt(1299)/243)^(1/3))))/2 + sqrt(-11/9 - 2/(27*(4/27 + sqrt(1299)/243)^(1/3)) + 2*(4/27 + sqrt(1299)/243)^(1/3))/2 + 1/6)
Respuesta numérica [src]
x1 = 1.10194069645862
x2 = -13.0833817091224
x3 = 49.7484713626735
x4 = 7.3851260036382
x5 = -31.9329376306611
x6 = -61.7299123753372
x7 = -93.1458389112352
x8 = 43.4652860554939
x9 = 38.8010525395361
x10 = 95.3497203041524
x11 = 68.5980272842123
x12 = -6.80019640194277
x13 = -99.4290242184148
x14 = -68.0130976825168
x15 = -57.0656788593795
x16 = 37.1821007483143
x17 = -30.3139858394393
x18 = 100.01395382011
x19 = 70.2169790754341
x20 = -80.579468296876
x21 = 62.3148419770327
x22 = 32.5178672323566
x23 = 81.1643978985714
x24 = 12.049359519596
x25 = 20218.7733074091
x26 = 82.7833496897932
x27 = -82.1984200880978
x28 = 74.8812125913918
x29 = -32074.5590524553
x30 = 18.3325448267756
x31 = 63.9337937682545
x32 = 30.8989154411347
x33 = 45.0842378467157
x34 = -11.4644299179006
x35 = -0.517011094763188
x36 = 87.447583205751
x37 = 26.234681925177
x38 = 56.0316566698531
x39 = 13.6683113108178
x40 = 24.6157301339552
x41 = -86.8626536040556
x42 = -63.3488641665591
x43 = -88.4816053952774
x44 = -24.0308005322597
x45 = -5.18124461072097
x46 = -17.7476152250801
x47 = 93.7307685129306
x48 = -94.764790702457
x49 = -69.6320494737386
x50 = 5974.79221603302
x51 = -50.7824935521999
x52 = -75.9152347809182
x53 = -36.5971711466189
x54 = -42.8803564537985
x55 = 57.6506084610749
x56 = -49.1635417609781
x57 = -55.4467270681577
x58 = 51.3674231538953
x59 = -19.3665670163019
x60 = -25.6497523234815
x61 = -38.2161229378407
x62 = 89.0665349969728
x63 = 5.7661742124164
x64 = -44.4993082450203
x65 = 19.9514966179974
x66 = 338.774995492934
x67 = -74.2962829896964
x68 = 76.5001643826137
x68 = 76.5001643826137