Sr Examen

sin(6x)=cos(2x) la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
sin(6*x) = cos(2*x)
$$\sin{\left(6 x \right)} = \cos{\left(2 x \right)}$$
Gráfica
Respuesta rápida [src]
     -7*pi
x1 = -----
       8  
$$x_{1} = - \frac{7 \pi}{8}$$
     -3*pi
x2 = -----
       8  
$$x_{2} = - \frac{3 \pi}{8}$$
     pi
x3 = --
     16
$$x_{3} = \frac{\pi}{16}$$
     pi
x4 = --
     8 
$$x_{4} = \frac{\pi}{8}$$
     5*pi
x5 = ----
      8  
$$x_{5} = \frac{5 \pi}{8}$$
           / 16____\
x6 = -I*log\-\/ -1 /
$$x_{6} = - i \log{\left(- \sqrt[16]{-1} \right)}$$
              /   /pi\\                                   
              |cos|--||        /    _____________________\
              |   \16/|        |   /    2/pi\      2/pi\ |
x7 = pi - atan|-------| - I*log|  /  cos |--| + sin |--| |
              |   /pi\|        \\/       \16/       \16/ /
              |sin|--||                                   
              \   \16//                                   
$$x_{7} = - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{16} \right)}}{\sin{\left(\frac{\pi}{16} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{16} \right)} + \cos^{2}{\left(\frac{\pi}{16} \right)}} \right)} + \pi$$
           /   /pi\\                                   
           |cos|--||        /    _____________________\
           |   \16/|        |   /    2/pi\      2/pi\ |
x8 = - atan|-------| - I*log|  /  cos |--| + sin |--| |
           |   /pi\|        \\/       \16/       \16/ /
           |sin|--||                                   
           \   \16//                                   
$$x_{8} = - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{16} \right)}}{\sin{\left(\frac{\pi}{16} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{16} \right)} + \cos^{2}{\left(\frac{\pi}{16} \right)}} \right)}$$
                                                      /   /3*pi\\
                /    _________________________\       |cos|----||
                |   /    2/3*pi\      2/3*pi\ |       |   \ 16 /|
x9 = -pi - I*log|  /  cos |----| + sin |----| | + atan|---------|
                \\/       \ 16 /       \ 16 / /       |   /3*pi\|
                                                      |sin|----||
                                                      \   \ 16 //
$$x_{9} = - \pi - i \log{\left(\sqrt{\sin^{2}{\left(\frac{3 \pi}{16} \right)} + \cos^{2}{\left(\frac{3 \pi}{16} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{3 \pi}{16} \right)}}{\sin{\left(\frac{3 \pi}{16} \right)}} \right)}$$
                                                   /   /5*pi\\
             /    _________________________\       |sin|----||
             |   /    2/3*pi\      2/5*pi\ |       |   \ 16 /|
x10 = - I*log|  /  sin |----| + sin |----| | + atan|---------|
             \\/       \ 16 /       \ 16 / /       |   /3*pi\|
                                                   |sin|----||
                                                   \   \ 16 //
$$x_{10} = - i \log{\left(\sqrt{\sin^{2}{\left(\frac{3 \pi}{16} \right)} + \sin^{2}{\left(\frac{5 \pi}{16} \right)}} \right)} + \operatorname{atan}{\left(\frac{\sin{\left(\frac{5 \pi}{16} \right)}}{\sin{\left(\frac{3 \pi}{16} \right)}} \right)}$$
               /   /3*pi\\                                       
               |sin|----||        /    _________________________\
               |   \ 16 /|        |   /    2/3*pi\      2/5*pi\ |
x11 = pi - atan|---------| - I*log|  /  sin |----| + sin |----| |
               |   /5*pi\|        \\/       \ 16 /       \ 16 / /
               |sin|----||                                       
               \   \ 16 //                                       
$$x_{11} = - \operatorname{atan}{\left(\frac{\sin{\left(\frac{3 \pi}{16} \right)}}{\sin{\left(\frac{5 \pi}{16} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{3 \pi}{16} \right)} + \sin^{2}{\left(\frac{5 \pi}{16} \right)}} \right)} + \pi$$
            /   /3*pi\\                                       
            |sin|----||        /    _________________________\
            |   \ 16 /|        |   /    2/3*pi\      2/5*pi\ |
x12 = - atan|---------| - I*log|  /  sin |----| + sin |----| |
            |   /5*pi\|        \\/       \ 16 /       \ 16 / /
            |sin|----||                                       
            \   \ 16 //                                       
$$x_{12} = - \operatorname{atan}{\left(\frac{\sin{\left(\frac{3 \pi}{16} \right)}}{\sin{\left(\frac{5 \pi}{16} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{3 \pi}{16} \right)} + \sin^{2}{\left(\frac{5 \pi}{16} \right)}} \right)}$$
x12 = -atan(sin(3*pi/16)/sin(5*pi/16)) - i*log(sqrt(sin(3*pi/16)^2 + sin(5*pi/16)^2))
Suma y producto de raíces [src]
suma
                                                           /   /pi\\                                            /   /pi\\                                                                                       /   /3*pi\\                                                /   /5*pi\\            /   /3*pi\\                                                /   /3*pi\\                                       
                                                           |cos|--||        /    _____________________\         |cos|--||        /    _____________________\              /    _________________________\       |cos|----||          /    _________________________\       |sin|----||            |sin|----||        /    _________________________\         |sin|----||        /    _________________________\
  7*pi   3*pi   pi   pi   5*pi        / 16____\            |   \16/|        |   /    2/pi\      2/pi\ |         |   \16/|        |   /    2/pi\      2/pi\ |              |   /    2/3*pi\      2/3*pi\ |       |   \ 16 /|          |   /    2/3*pi\      2/5*pi\ |       |   \ 16 /|            |   \ 16 /|        |   /    2/3*pi\      2/5*pi\ |         |   \ 16 /|        |   /    2/3*pi\      2/5*pi\ |
- ---- - ---- + -- + -- + ---- - I*log\-\/ -1 / + pi - atan|-------| - I*log|  /  cos |--| + sin |--| | + - atan|-------| - I*log|  /  cos |--| + sin |--| | + -pi - I*log|  /  cos |----| + sin |----| | + atan|---------| + - I*log|  /  sin |----| + sin |----| | + atan|---------| + pi - atan|---------| - I*log|  /  sin |----| + sin |----| | + - atan|---------| - I*log|  /  sin |----| + sin |----| |
   8      8     16   8     8                               |   /pi\|        \\/       \16/       \16/ /         |   /pi\|        \\/       \16/       \16/ /              \\/       \ 16 /       \ 16 / /       |   /3*pi\|          \\/       \ 16 /       \ 16 / /       |   /3*pi\|            |   /5*pi\|        \\/       \ 16 /       \ 16 / /         |   /5*pi\|        \\/       \ 16 /       \ 16 / /
                                                           |sin|--||                                            |sin|--||                                                                                       |sin|----||                                                |sin|----||            |sin|----||                                                |sin|----||                                       
                                                           \   \16//                                            \   \16//                                                                                       \   \ 16 //                                                \   \ 16 //            \   \ 16 //                                                \   \ 16 //                                       
$$\left(- \operatorname{atan}{\left(\frac{\sin{\left(\frac{3 \pi}{16} \right)}}{\sin{\left(\frac{5 \pi}{16} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{3 \pi}{16} \right)} + \sin^{2}{\left(\frac{5 \pi}{16} \right)}} \right)}\right) + \left(\left(\left(\left(\left(\left(- i \log{\left(- \sqrt[16]{-1} \right)} + \left(\left(\left(\left(- \frac{7 \pi}{8} - \frac{3 \pi}{8}\right) + \frac{\pi}{16}\right) + \frac{\pi}{8}\right) + \frac{5 \pi}{8}\right)\right) + \left(- \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{16} \right)}}{\sin{\left(\frac{\pi}{16} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{16} \right)} + \cos^{2}{\left(\frac{\pi}{16} \right)}} \right)} + \pi\right)\right) + \left(- \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{16} \right)}}{\sin{\left(\frac{\pi}{16} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{16} \right)} + \cos^{2}{\left(\frac{\pi}{16} \right)}} \right)}\right)\right) + \left(- \pi - i \log{\left(\sqrt{\sin^{2}{\left(\frac{3 \pi}{16} \right)} + \cos^{2}{\left(\frac{3 \pi}{16} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{3 \pi}{16} \right)}}{\sin{\left(\frac{3 \pi}{16} \right)}} \right)}\right)\right) + \left(- i \log{\left(\sqrt{\sin^{2}{\left(\frac{3 \pi}{16} \right)} + \sin^{2}{\left(\frac{5 \pi}{16} \right)}} \right)} + \operatorname{atan}{\left(\frac{\sin{\left(\frac{5 \pi}{16} \right)}}{\sin{\left(\frac{3 \pi}{16} \right)}} \right)}\right)\right) + \left(- \operatorname{atan}{\left(\frac{\sin{\left(\frac{3 \pi}{16} \right)}}{\sin{\left(\frac{5 \pi}{16} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{3 \pi}{16} \right)} + \sin^{2}{\left(\frac{5 \pi}{16} \right)}} \right)} + \pi\right)\right)$$
=
        /   /pi\\         /   /3*pi\\                                                                                                                                                    /   /3*pi\\       /   /5*pi\\
        |cos|--||         |sin|----||               /    _________________________\                           /    _________________________\          /    _____________________\       |cos|----||       |sin|----||
        |   \16/|         |   \ 16 /|   9*pi        |   /    2/3*pi\      2/3*pi\ |        / 16____\          |   /    2/3*pi\      2/5*pi\ |          |   /    2/pi\      2/pi\ |       |   \ 16 /|       |   \ 16 /|
- 2*atan|-------| - 2*atan|---------| + ---- - I*log|  /  cos |----| + sin |----| | - I*log\-\/ -1 / - 3*I*log|  /  sin |----| + sin |----| | - 2*I*log|  /  cos |--| + sin |--| | + atan|---------| + atan|---------|
        |   /pi\|         |   /5*pi\|    16         \\/       \ 16 /       \ 16 / /                           \\/       \ 16 /       \ 16 / /          \\/       \16/       \16/ /       |   /3*pi\|       |   /3*pi\|
        |sin|--||         |sin|----||                                                                                                                                                    |sin|----||       |sin|----||
        \   \16//         \   \ 16 //                                                                                                                                                    \   \ 16 //       \   \ 16 //
$$- i \log{\left(- \sqrt[16]{-1} \right)} - 2 \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{16} \right)}}{\sin{\left(\frac{\pi}{16} \right)}} \right)} - 2 \operatorname{atan}{\left(\frac{\sin{\left(\frac{3 \pi}{16} \right)}}{\sin{\left(\frac{5 \pi}{16} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{3 \pi}{16} \right)} + \cos^{2}{\left(\frac{3 \pi}{16} \right)}} \right)} - 3 i \log{\left(\sqrt{\sin^{2}{\left(\frac{3 \pi}{16} \right)} + \sin^{2}{\left(\frac{5 \pi}{16} \right)}} \right)} - 2 i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{16} \right)} + \cos^{2}{\left(\frac{\pi}{16} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{3 \pi}{16} \right)}}{\sin{\left(\frac{3 \pi}{16} \right)}} \right)} + \operatorname{atan}{\left(\frac{\sin{\left(\frac{5 \pi}{16} \right)}}{\sin{\left(\frac{3 \pi}{16} \right)}} \right)} + \frac{9 \pi}{16}$$
producto
                                         /         /   /pi\\                                   \ /      /   /pi\\                                   \ /                                                 /   /3*pi\\\ /                                             /   /5*pi\\\ /         /   /3*pi\\                                       \ /      /   /3*pi\\                                       \
                                         |         |cos|--||        /    _____________________\| |      |cos|--||        /    _____________________\| |           /    _________________________\       |cos|----||| |       /    _________________________\       |sin|----||| |         |sin|----||        /    _________________________\| |      |sin|----||        /    _________________________\|
-7*pi -3*pi pi pi 5*pi /      / 16____\\ |         |   \16/|        |   /    2/pi\      2/pi\ || |      |   \16/|        |   /    2/pi\      2/pi\ || |           |   /    2/3*pi\      2/3*pi\ |       |   \ 16 /|| |       |   /    2/3*pi\      2/5*pi\ |       |   \ 16 /|| |         |   \ 16 /|        |   /    2/3*pi\      2/5*pi\ || |      |   \ 16 /|        |   /    2/3*pi\      2/5*pi\ ||
-----*-----*--*--*----*\-I*log\-\/ -1 //*|pi - atan|-------| - I*log|  /  cos |--| + sin |--| ||*|- atan|-------| - I*log|  /  cos |--| + sin |--| ||*|-pi - I*log|  /  cos |----| + sin |----| | + atan|---------||*|- I*log|  /  sin |----| + sin |----| | + atan|---------||*|pi - atan|---------| - I*log|  /  sin |----| + sin |----| ||*|- atan|---------| - I*log|  /  sin |----| + sin |----| ||
  8     8   16 8   8                     |         |   /pi\|        \\/       \16/       \16/ /| |      |   /pi\|        \\/       \16/       \16/ /| |           \\/       \ 16 /       \ 16 / /       |   /3*pi\|| |       \\/       \ 16 /       \ 16 / /       |   /3*pi\|| |         |   /5*pi\|        \\/       \ 16 /       \ 16 / /| |      |   /5*pi\|        \\/       \ 16 /       \ 16 / /|
                                         |         |sin|--||                                   | |      |sin|--||                                   | |                                                 |sin|----||| |                                             |sin|----||| |         |sin|----||                                       | |      |sin|----||                                       |
                                         \         \   \16//                                   / \      \   \16//                                   / \                                                 \   \ 16 /// \                                             \   \ 16 /// \         \   \ 16 //                                       / \      \   \ 16 //                                       /
$$- i \log{\left(- \sqrt[16]{-1} \right)} \frac{5 \pi}{8} \frac{\pi}{8} \frac{\pi}{16} \cdot - \frac{7 \pi}{8} \left(- \frac{3 \pi}{8}\right) \left(- \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{16} \right)}}{\sin{\left(\frac{\pi}{16} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{16} \right)} + \cos^{2}{\left(\frac{\pi}{16} \right)}} \right)} + \pi\right) \left(- \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{16} \right)}}{\sin{\left(\frac{\pi}{16} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{16} \right)} + \cos^{2}{\left(\frac{\pi}{16} \right)}} \right)}\right) \left(- \pi - i \log{\left(\sqrt{\sin^{2}{\left(\frac{3 \pi}{16} \right)} + \cos^{2}{\left(\frac{3 \pi}{16} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{3 \pi}{16} \right)}}{\sin{\left(\frac{3 \pi}{16} \right)}} \right)}\right) \left(- i \log{\left(\sqrt{\sin^{2}{\left(\frac{3 \pi}{16} \right)} + \sin^{2}{\left(\frac{5 \pi}{16} \right)}} \right)} + \operatorname{atan}{\left(\frac{\sin{\left(\frac{5 \pi}{16} \right)}}{\sin{\left(\frac{3 \pi}{16} \right)}} \right)}\right) \left(- \operatorname{atan}{\left(\frac{\sin{\left(\frac{3 \pi}{16} \right)}}{\sin{\left(\frac{5 \pi}{16} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{3 \pi}{16} \right)} + \sin^{2}{\left(\frac{5 \pi}{16} \right)}} \right)} + \pi\right) \left(- \operatorname{atan}{\left(\frac{\sin{\left(\frac{3 \pi}{16} \right)}}{\sin{\left(\frac{5 \pi}{16} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{3 \pi}{16} \right)} + \sin^{2}{\left(\frac{5 \pi}{16} \right)}} \right)}\right)$$
=
          /         /      ___________  \\ /          /      ___________  \\ /          /       ___________\\     /      ___________  \     /      ___________  \     /       ___________\             
          |         |     /       ___   || |          |     /       ___   || |          |      /       ___ ||     |     /       ___   |     |     /       ___   |     |      /       ___ |             
        5 |         |   \/  2 + \/ 2    || |          |   \/  2 - \/ 2    || |          |2 - \/  2 - \/ 2  ||     |   \/  2 - \/ 2    |     |   \/  2 + \/ 2    |     |2 - \/  2 - \/ 2  |    / 16____\
105*I*pi *|pi + atan|-------------------||*|-pi - atan|-------------------||*|-pi + atan|------------------||*atan|-------------------|*atan|-------------------|*atan|------------------|*log\-\/ -1 /
          |         |        ___________|| |          |        ___________|| |          |     ___________  ||     |        ___________|     |        ___________|     |     ___________  |             
          |         |       /       ___ || |          |       /       ___ || |          |    /       ___   ||     |       /       ___ |     |       /       ___ |     |    /       ___   |             
          \         \-2 + \/  2 - \/ 2  // \          \-2 + \/  2 + \/ 2  // \          \  \/  2 + \/ 2    //     \-2 + \/  2 + \/ 2  /     \-2 + \/  2 - \/ 2  /     \  \/  2 + \/ 2    /             
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                 65536                                                                                                 
$$\frac{105 i \pi^{5} \left(- \pi - \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}}}{-2 + \sqrt{\sqrt{2} + 2}} \right)}\right) \left(- \pi + \operatorname{atan}{\left(\frac{2 - \sqrt{2 - \sqrt{2}}}{\sqrt{\sqrt{2} + 2}} \right)}\right) \left(\operatorname{atan}{\left(\frac{\sqrt{\sqrt{2} + 2}}{-2 + \sqrt{2 - \sqrt{2}}} \right)} + \pi\right) \log{\left(- \sqrt[16]{-1} \right)} \operatorname{atan}{\left(\frac{\sqrt{\sqrt{2} + 2}}{-2 + \sqrt{2 - \sqrt{2}}} \right)} \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}}}{-2 + \sqrt{\sqrt{2} + 2}} \right)} \operatorname{atan}{\left(\frac{2 - \sqrt{2 - \sqrt{2}}}{\sqrt{\sqrt{2} + 2}} \right)}}{65536}$$
105*i*pi^5*(pi + atan(sqrt(2 + sqrt(2))/(-2 + sqrt(2 - sqrt(2)))))*(-pi - atan(sqrt(2 - sqrt(2))/(-2 + sqrt(2 + sqrt(2)))))*(-pi + atan((2 - sqrt(2 - sqrt(2)))/sqrt(2 + sqrt(2))))*atan(sqrt(2 - sqrt(2))/(-2 + sqrt(2 + sqrt(2))))*atan(sqrt(2 + sqrt(2))/(-2 + sqrt(2 - sqrt(2))))*atan((2 - sqrt(2 - sqrt(2)))/sqrt(2 + sqrt(2)))*log(-(-1)^(1/16))/65536
Respuesta numérica [src]
x1 = 1.96349540849362
x2 = 6.67588438887831
x3 = 66.169795266235
x4 = 45.9457925587507
x5 = 92.0879346583508
x6 = -17.8678082172919
x7 = 40.2516558741192
x8 = 82.0741080750334
x9 = -10.0138265833175
x10 = 88.1609438413636
x11 = -93.8550805259951
x12 = -43.7859476094077
x13 = 70.0967860832223
x14 = 8.05033117482385
x15 = 23.9546439836222
x16 = -90.1244392498572
x17 = -3.73064127613788
x18 = 22.1874981159779
x19 = -15.3152641862502
x20 = 16.1006623496477
x21 = -7.65763209312512
x22 = -56.3523182237669
x23 = 80.3069622073891
x24 = -24.1509935244715
x25 = 62.2428044492478
x26 = -53.9961237335746
x27 = 41.233403578366
x28 = -73.6310778185108
x29 = -71.8639319508665
x30 = -91.6952355766521
x31 = -47.712938426395
x32 = 30.8268779133498
x33 = -55.5669200603695
x34 = -68.1332906747286
x35 = -2.15984494934298
x36 = 44.1786466911065
x37 = 89.9280897090078
x38 = -21.7947990342792
x39 = -42.0188017417635
x40 = -100.334615374024
x41 = 18.2605072989907
x42 = 36.324665057132
x43 = -13.7444678594553
x44 = -5.89048622548086
x45 = -39.8589567924205
x46 = 84.2339530243763
x47 = 52.2289778659303
x48 = 58.3158136322605
x49 = 60.0829594999048
x50 = -20.0276531666349
x51 = -87.7682447596649
x52 = -27.8816348006094
x53 = -25.7217898512664
x54 = 67.9369411338793
x55 = 33.9684705669396
x56 = 94.4441291485432
x57 = -49.872783375738
x58 = -57.7267650097125
x59 = -46.1421420996001
x60 = 72.4529805734146
x61 = 63.0282026126452
x62 = 96.0149254753381
x63 = 30.2378292908018
x64 = -79.717913584841
x65 = -65.7770961845363
x66 = 4.1233403578366
x67 = -61.8501053675491
x68 = 99.9419162923253
x69 = -32.004975158446
x70 = 7.2649330114264
x71 = 166.897109721958
x72 = 48.1056375080937
x73 = 85.2157007286231
x74 = -83.8412539426776
x75 = 26.1144889329652
x76 = 55.9596191420682
x77 = -10.6028752058656
x78 = -97.9784208838317
x79 = 0.196349540849362
x80 = 11.9773219918111
x81 = 38.0918109247762
x82 = -64.009950316892
x83 = -80.6996612890878
x84 = -78.3434667988955
x85 = -69.7040870015235
x86 = 28.6670329640069
x87 = 8.24668071567321
x88 = 77.9507677171967
x89 = 50.6581815391354
x90 = -86.0010988920206
x91 = -51.6399292433822
x92 = -35.7356164345839
x93 = -75.9872723087031
x94 = -95.6222263936393
x95 = -29.6487806682537
x96 = 14.3335164820034
x96 = 14.3335164820034