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sin(x)^3+3*sin(x)^2*cos(x)-sin(x)*cos(x)^2-3*cos(x)^3=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
   3           2                       2           3       
sin (x) + 3*sin (x)*cos(x) - sin(x)*cos (x) - 3*cos (x) = 0
$$\left(\left(\sin^{3}{\left(x \right)} + 3 \sin^{2}{\left(x \right)} \cos{\left(x \right)}\right) - \sin{\left(x \right)} \cos^{2}{\left(x \right)}\right) - 3 \cos^{3}{\left(x \right)} = 0$$
Gráfica
Respuesta rápida [src]
     -3*pi
x1 = -----
       4  
$$x_{1} = - \frac{3 \pi}{4}$$
     -pi 
x2 = ----
      4  
$$x_{2} = - \frac{\pi}{4}$$
     pi
x3 = --
     4 
$$x_{3} = \frac{\pi}{4}$$
     3*pi
x4 = ----
      4  
$$x_{4} = \frac{3 \pi}{4}$$
           /      ____\
           |1   \/ 10 |
x5 = 2*atan|- - ------|
           \3     3   /
$$x_{5} = 2 \operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{10}}{3} \right)}$$
           /      ____\
           |1   \/ 10 |
x6 = 2*atan|- + ------|
           \3     3   /
$$x_{6} = 2 \operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{10}}{3} \right)}$$
x6 = 2*atan(1/3 + sqrt(10)/3)
Suma y producto de raíces [src]
suma
                                /      ____\         /      ____\
  3*pi   pi   pi   3*pi         |1   \/ 10 |         |1   \/ 10 |
- ---- - -- + -- + ---- + 2*atan|- - ------| + 2*atan|- + ------|
   4     4    4     4           \3     3   /         \3     3   /
$$\left(2 \operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{10}}{3} \right)} + \left(\left(\left(- \frac{3 \pi}{4} - \frac{\pi}{4}\right) + \frac{\pi}{4}\right) + \frac{3 \pi}{4}\right)\right) + 2 \operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{10}}{3} \right)}$$
=
      /      ____\         /      ____\
      |1   \/ 10 |         |1   \/ 10 |
2*atan|- - ------| + 2*atan|- + ------|
      \3     3   /         \3     3   /
$$2 \operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{10}}{3} \right)} + 2 \operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{10}}{3} \right)}$$
producto
                         /      ____\       /      ____\
-3*pi -pi  pi 3*pi       |1   \/ 10 |       |1   \/ 10 |
-----*----*--*----*2*atan|- - ------|*2*atan|- + ------|
  4    4   4   4         \3     3   /       \3     3   /
$$\frac{3 \pi}{4} \frac{\pi}{4} \cdot - \frac{3 \pi}{4} \left(- \frac{\pi}{4}\right) 2 \operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{10}}{3} \right)} 2 \operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{10}}{3} \right)}$$
=
          /      ____\     /      ____\
    4     |1   \/ 10 |     |1   \/ 10 |
9*pi *atan|- - ------|*atan|- + ------|
          \3     3   /     \3     3   /
---------------------------------------
                   64                  
$$\frac{9 \pi^{4} \operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{10}}{3} \right)} \operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{10}}{3} \right)}}{64}$$
9*pi^4*atan(1/3 - sqrt(10)/3)*atan(1/3 + sqrt(10)/3)/64
Respuesta numérica [src]
x1 = 71.007585260167
x2 = 99.7455667514759
x3 = 58.4412146458078
x4 = -25.9181393921158
x5 = -38.484510006475
x6 = -84.037603483527
x7 = -55.7632696012188
x8 = -71.4712328691678
x9 = -64.0808988441941
x10 = 45.8748440314486
x11 = 1.89254688119154
x12 = 96.1403264888853
x13 = 14.4589174955507
x14 = 5.49778714378214
x15 = 82.4668071567321
x16 = -11.7809724509617
x17 = 60.4756585816035
x18 = 38.484510006475
x19 = 76.1836218495525
x20 = 23.8836954563201
x21 = -10.2101761241668
x22 = -77.7544181763474
x23 = -13.8154163867574
x24 = -95.496825380092
x25 = 16.4933614313464
x26 = 69.9004365423729
x27 = -82.9304547657329
x28 = 32.2013246992954
x29 = 36.4500660706793
x30 = 68.329640215578
x31 = -16.4933614313464
x32 = -79.7888621121431
x33 = 11.7809724509617
x34 = -3.92699081698724
x35 = 90.3207887907066
x36 = -82.4668071567321
x37 = -35.806564961886
x38 = -27.4889357189107
x39 = -18.0641577581413
x40 = 30.1668807634997
x41 = -62.0464549083984
x42 = -47.9092879672443
x43 = -32.2013246992954
x44 = -73.5056768049635
x45 = -49.4800842940392
x46 = -93.4623814442964
x47 = 47.9092879672443
x48 = -58.9048622548086
x49 = 77.7544181763474
x50 = 54.1924732744239
x51 = -98.174770424681
x52 = -51.5145282298349
x53 = 27.4889357189107
x54 = 92.9987338352955
x55 = 55.7632696012188
x56 = -42.0897502690656
x57 = -76.1836218495525
x58 = -5.49778714378214
x59 = -60.4756585816035
x60 = 84.037603483527
x61 = -7.53223107957784
x62 = 43.1968989868597
x63 = 3.92699081698724
x64 = -86.0720474193227
x65 = -23.2401943475268
x66 = 10.2101761241668
x67 = -69.9004365423729
x68 = -33.7721210260903
x69 = 74.1491779137568
x70 = -54.1924732744239
x71 = 33.7721210260903
x72 = 46.3384916404494
x73 = -91.8915851175014
x74 = 2.35619449019234
x75 = 88.7499924639117
x76 = -57.7977135370145
x77 = 25.9181393921158
x78 = 80.4323632209364
x79 = 40.0553063332699
x80 = 91.8915851175014
x81 = -90.3207887907066
x82 = -40.0553063332699
x83 = 98.174770424681
x84 = 18.0641577581413
x85 = -29.5233796547064
x86 = 62.0464549083984
x87 = 8.17573218837112
x88 = 52.1580293386282
x89 = -99.7455667514759
x89 = -99.7455667514759