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tg(2x)cos(3x)+sin(3x)+(2)^(1/2)*sin(5x)=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
                                 ___             
tan(2*x)*cos(3*x) + sin(3*x) + \/ 2 *sin(5*x) = 0
$$\left(\sin{\left(3 x \right)} + \cos{\left(3 x \right)} \tan{\left(2 x \right)}\right) + \sqrt{2} \sin{\left(5 x \right)} = 0$$
Simplificar
Gráfica
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
x1 = 0
$$x_{1} = 0$$ 
     -4*pi
x2 = -----
       5
$$x_{2} = - \frac{4 \pi}{5}$$ 
     -3*pi
x3 = -----
       5
$$x_{3} = - \frac{3 \pi}{5}$$ 
     -2*pi
x4 = -----
       5
$$x_{4} = - \frac{2 \pi}{5}$$ 
     -3*pi
x5 = -----
       8
$$x_{5} = - \frac{3 \pi}{8}$$ 
     -pi 
x6 = ----
      5
$$x_{6} = - \frac{\pi}{5}$$ 
     pi
x7 = --
     5
$$x_{7} = \frac{\pi}{5}$$ 
     3*pi
x8 = ----
      8
$$x_{8} = \frac{3 \pi}{8}$$ 
     2*pi
x9 = ----
      5
$$x_{9} = \frac{2 \pi}{5}$$ 
      3*pi
x10 = ----
       5
$$x_{10} = \frac{3 \pi}{5}$$ 
      4*pi
x11 = ----
       5
$$x_{11} = \frac{4 \pi}{5}$$ 
x12 = pi
$$x_{12} = \pi$$ 
               /     ___________\                            
               |    /       ___ |                            
               |   /  1   \/ 2  |                            
               |  /   - + ----- |                            
               |\/    2     4   |     /     /4 ___\   log(2)\
x13 = pi - atan|----------------| + I*|- log\\/ 2 / + ------|
               |     ___________|     \                 4   /
               |    /       ___ |                            
               |   /  1   \/ 2  |                            
               |  /   - - ----- |                            
               \\/    2     4   /
$$x_{13} = - \operatorname{atan}{\left(\frac{\sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{\sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}} \right)} + \pi + i \left(- \log{\left(\sqrt[4]{2} \right)} + \frac{\log{\left(2 \right)}}{4}\right)$$ 
                                            /     ___________\
                                            |    /       ___ |
                                            |   /  1   \/ 2  |
                                            |  /   - + ----- |
              /     /4 ___\   log(2)\       |\/    2     4   |
x14 = -pi + I*|- log\\/ 2 / + ------| + atan|----------------|
              \                 4   /       |     ___________|
                                            |    /       ___ |
                                            |   /  1   \/ 2  |
                                            |  /   - - ----- |
                                            \\/    2     4   /
$$x_{14} = - \pi + \operatorname{atan}{\left(\frac{\sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{\sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}} \right)} + i \left(- \log{\left(\sqrt[4]{2} \right)} + \frac{\log{\left(2 \right)}}{4}\right)$$ 
x14 = -pi + atan(sqrt(sqrt(2)/4 + 1/2)/sqrt(1/2 - sqrt(2)/4)) + i*(-log(2^(1/4)) + log(2)/4)
Suma y producto de raíces [src] 
suma
                                                                                  /     ___________\                                                                     /     ___________\
                                                                                  |    /       ___ |                                                                     |    /       ___ |
                                                                                  |   /  1   \/ 2  |                                                                     |   /  1   \/ 2  |
                                                                                  |  /   - + ----- |                                                                     |  /   - + ----- |
  4*pi   3*pi   2*pi   3*pi   pi   pi   3*pi   2*pi   3*pi   4*pi                 |\/    2     4   |     /     /4 ___\   log(2)\           /     /4 ___\   log(2)\       |\/    2     4   |
- ---- - ---- - ---- - ---- - -- + -- + ---- + ---- + ---- + ---- + pi + pi - atan|----------------| + I*|- log\\/ 2 / + ------| + -pi + I*|- log\\/ 2 / + ------| + atan|----------------|
   5      5      5      8     5    5     8      5      5      5                   |     ___________|     \                 4   /           \                 4   /       |     ___________|
                                                                                  |    /       ___ |                                                                     |    /       ___ |
                                                                                  |   /  1   \/ 2  |                                                                     |   /  1   \/ 2  |
                                                                                  |  /   - - ----- |                                                                     |  /   - - ----- |
                                                                                  \\/    2     4   /                                                                     \\/    2     4   /
$$\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(- \frac{4 \pi}{5} - \frac{3 \pi}{5}\right) - \frac{2 \pi}{5}\right) - \frac{3 \pi}{8}\right) - \frac{\pi}{5}\right) + \frac{\pi}{5}\right) + \frac{3 \pi}{8}\right) + \frac{2 \pi}{5}\right) + \frac{3 \pi}{5}\right) + \frac{4 \pi}{5}\right) + \pi\right) + \left(- \operatorname{atan}{\left(\frac{\sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{\sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}} \right)} + \pi + i \left(- \log{\left(\sqrt[4]{2} \right)} + \frac{\log{\left(2 \right)}}{4}\right)\right)\right) + \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{\sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}} \right)} + i \left(- \log{\left(\sqrt[4]{2} \right)} + \frac{\log{\left(2 \right)}}{4}\right)\right)$$ 
=
         /     /4 ___\   log(2)\
pi + 2*I*|- log\\/ 2 / + ------|
         \                 4   /
$$\pi + 2 i \left(- \log{\left(\sqrt[4]{2} \right)} + \frac{\log{\left(2 \right)}}{4}\right)$$ 
producto
                                                         /         /     ___________\                            \ /                                      /     ___________\\
                                                         |         |    /       ___ |                            | |                                      |    /       ___ ||
                                                         |         |   /  1   \/ 2  |                            | |                                      |   /  1   \/ 2  ||
                                                         |         |  /   - + ----- |                            | |                                      |  /   - + ----- ||
  -4*pi -3*pi -2*pi -3*pi -pi  pi 3*pi 2*pi 3*pi 4*pi    |         |\/    2     4   |     /     /4 ___\   log(2)\| |        /     /4 ___\   log(2)\       |\/    2     4   ||
0*-----*-----*-----*-----*----*--*----*----*----*----*pi*|pi - atan|----------------| + I*|- log\\/ 2 / + ------||*|-pi + I*|- log\\/ 2 / + ------| + atan|----------------||
    5     5     5     8    5   5   8    5    5    5      |         |     ___________|     \                 4   /| |        \                 4   /       |     ___________||
                                                         |         |    /       ___ |                            | |                                      |    /       ___ ||
                                                         |         |   /  1   \/ 2  |                            | |                                      |   /  1   \/ 2  ||
                                                         |         |  /   - - ----- |                            | |                                      |  /   - - ----- ||
                                                         \         \\/    2     4   /                            / \                                      \\/    2     4   //
$$\pi \frac{4 \pi}{5} \frac{3 \pi}{5} \frac{2 \pi}{5} \frac{3 \pi}{8} \frac{\pi}{5} \cdot - \frac{\pi}{5} \cdot - \frac{3 \pi}{8} \cdot - \frac{2 \pi}{5} \cdot - \frac{3 \pi}{5} \cdot 0 \left(- \frac{4 \pi}{5}\right) \left(- \operatorname{atan}{\left(\frac{\sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{\sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}} \right)} + \pi + i \left(- \log{\left(\sqrt[4]{2} \right)} + \frac{\log{\left(2 \right)}}{4}\right)\right) \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{\sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}} \right)} + i \left(- \log{\left(\sqrt[4]{2} \right)} + \frac{\log{\left(2 \right)}}{4}\right)\right)$$ 
=
0
$$0$$ 
0
Respuesta numérica [src] 
x1 = 65.9734457253857
x2 = 26.3108384738145
x3 = 4.31968989868597
x4 = -21.9911485751286
x5 = 21.9911485751286
x6 = -76.026542216873
x7 = -86.0010988920206
x8 = -15.707963267949
x9 = -92.3628240155399
x10 = 48.3019870489431
x11 = -73.4347282776614
x12 = 6.28318530717959
x13 = 13.7444678594553
x14 = -32.0442450666159
x15 = 64.009950316892
x16 = -77.9114978090269
x17 = -33.9292006587698
x18 = 89.9280897090078
x19 = -1.96349540849362
x20 = 18.2212373908208
x21 = 28.2743338823081
x22 = -39.6626072515711
x23 = -99.9026463841554
x24 = -8.24668071567321
x25 = -42.0188017417635
x26 = -57.7267650097125
x27 = 92.2842841992002
x28 = -35.7356164345839
x29 = -10.0530964914873
x30 = 74.2201264410589
x31 = 38.3274303737955
x32 = -13.7444678594553
x33 = -20.0276531666349
x34 = 42.0188017417635
x35 = 52.2289778659303
x36 = -64.009950316892
x37 = 56.5486677646163
x38 = 23.9546439836222
x39 = 61.6537558266997
x40 = 72.2566310325652
x41 = -61.6537558266997
x42 = -559.203492338983
x43 = -87.9645943005142
x44 = -69.7433569096934
x45 = -37.6991118430775
x46 = -43.9822971502571
x47 = 40.2123859659494
x48 = -55.9203492338983
x49 = 98.0176907920015
x50 = -47.7522083345649
x51 = 62.2035345410779
x52 = -79.7964534011807
x53 = -49.0873852123405
x54 = -29.4524311274043
x55 = 96.2112750161874
x56 = -11.9380520836412
x57 = -45.867252742411
x58 = -25.7610597594363
x59 = 76.026542216873
x60 = -81.6814089933346
x61 = 70.2931356240716
x62 = 30.2378292908018
x63 = -3.76991118430775
x64 = -65.9734457253857
x65 = 54.0353936417444
x66 = 1.96349540849362
x67 = 0.0
x68 = 80.4247719318987
x69 = -1135.37158500735
x70 = -98.0176907920015
x71 = 13.8230076757951
x72 = 60.318578948924
x73 = 67.9369411338793
x74 = 43.9822971502571
x75 = 45.9457925587507
x76 = -54.0353936417444
x77 = 84.1946831162065
x78 = 8.24668071567321
x79 = -67.8584013175395
x80 = -23.9546439836222
x81 = 50.2654824574367
x82 = 94.2477796076938
x83 = 82.3097275240526
x84 = -59.6902604182061
x85 = 86.0010988920206
x86 = -7.5398223686155
x87 = 10.0530964914873
x88 = -17.6714586764426
x89 = 34.5575191894877
x90 = -89.8495498926681
x91 = -27.0176968208722
x92 = -51.5221195188726
x93 = 15.707963267949
x94 = 87.9645943005142
x95 = 32.0442450666159
x96 = -83.6449044018282
x97 = -98.6460093227195
x98 = 80.5033117482384
x99 = -91.734505484822
x100 = 98.6460093227195
x101 = -70.9999939711293
x101 = -70.9999939711293
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