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3*sin^2x+11*sinx*cosx+6cos^2x=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
     2                              2       
3*sin (x) + 11*sin(x)*cos(x) + 6*cos (x) = 0
$$\left(3 \sin^{2}{\left(x \right)} + 11 \sin{\left(x \right)} \cos{\left(x \right)}\right) + 6 \cos^{2}{\left(x \right)} = 0$$
Simplificar
Gráfica
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
           /      ____\
           |1   \/ 10 |
x1 = 2*atan|- - ------|
           \3     3   /
$$x_{1} = 2 \operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{10}}{3} \right)}$$ 
           /      ____\
           |1   \/ 10 |
x2 = 2*atan|- + ------|
           \3     3   /
$$x_{2} = 2 \operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{10}}{3} \right)}$$ 
           /      ____\
           |3   \/ 13 |
x3 = 2*atan|- - ------|
           \2     2   /
$$x_{3} = 2 \operatorname{atan}{\left(\frac{3}{2} - \frac{\sqrt{13}}{2} \right)}$$ 
           /      ____\
           |3   \/ 13 |
x4 = 2*atan|- + ------|
           \2     2   /
$$x_{4} = 2 \operatorname{atan}{\left(\frac{3}{2} + \frac{\sqrt{13}}{2} \right)}$$ 
x4 = 2*atan(3/2 + sqrt(13)/2)
Suma y producto de raíces [src] 
suma
      /      ____\         /      ____\         /      ____\         /      ____\
      |1   \/ 10 |         |1   \/ 10 |         |3   \/ 13 |         |3   \/ 13 |
2*atan|- - ------| + 2*atan|- + ------| + 2*atan|- - ------| + 2*atan|- + ------|
      \3     3   /         \3     3   /         \2     2   /         \2     2   /
$$\left(2 \operatorname{atan}{\left(\frac{3}{2} - \frac{\sqrt{13}}{2} \right)} + \left(2 \operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{10}}{3} \right)} + 2 \operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{10}}{3} \right)}\right)\right) + 2 \operatorname{atan}{\left(\frac{3}{2} + \frac{\sqrt{13}}{2} \right)}$$ 
=
      /      ____\         /      ____\         /      ____\         /      ____\
      |1   \/ 10 |         |1   \/ 10 |         |3   \/ 13 |         |3   \/ 13 |
2*atan|- - ------| + 2*atan|- + ------| + 2*atan|- + ------| + 2*atan|- - ------|
      \3     3   /         \3     3   /         \2     2   /         \2     2   /
$$2 \operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{10}}{3} \right)} + 2 \operatorname{atan}{\left(\frac{3}{2} - \frac{\sqrt{13}}{2} \right)} + 2 \operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{10}}{3} \right)} + 2 \operatorname{atan}{\left(\frac{3}{2} + \frac{\sqrt{13}}{2} \right)}$$ 
producto
      /      ____\       /      ____\       /      ____\       /      ____\
      |1   \/ 10 |       |1   \/ 10 |       |3   \/ 13 |       |3   \/ 13 |
2*atan|- - ------|*2*atan|- + ------|*2*atan|- - ------|*2*atan|- + ------|
      \3     3   /       \3     3   /       \2     2   /       \2     2   /
$$2 \operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{10}}{3} \right)} 2 \operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{10}}{3} \right)} 2 \operatorname{atan}{\left(\frac{3}{2} - \frac{\sqrt{13}}{2} \right)} 2 \operatorname{atan}{\left(\frac{3}{2} + \frac{\sqrt{13}}{2} \right)}$$ 
=
       /      ____\     /      ____\     /      ____\     /      ____\
       |1   \/ 10 |     |1   \/ 10 |     |3   \/ 13 |     |3   \/ 13 |
16*atan|- - ------|*atan|- + ------|*atan|- + ------|*atan|- - ------|
       \3     3   /     \3     3   /     \2     2   /     \2     2   /
$$16 \operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{10}}{3} \right)} \operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{10}}{3} \right)} \operatorname{atan}{\left(\frac{3}{2} - \frac{\sqrt{13}}{2} \right)} \operatorname{atan}{\left(\frac{3}{2} + \frac{\sqrt{13}}{2} \right)}$$ 
16*atan(1/3 - sqrt(10)/3)*atan(1/3 + sqrt(10)/3)*atan(3/2 + sqrt(13)/2)*atan(3/2 - sqrt(13)/2)
Respuesta numérica [src] 
x1 = -13.8154163867574
x2 = 49.0164366850384
x3 = -51.5145282298349
x4 = -86.0720474193227
x5 = -3.72959525713736
x6 = 89.8571411817058
x7 = -42.0897502690656
x8 = 20.7421028027303
x9 = 86.715548528116
x10 = 55.9606651610687
x11 = 49.6774798538891
x12 = -35.1455217930353
x13 = -79.7888621121431
x14 = 71.6686284290177
x15 = -75.9862262897026
x16 = 93.6597770041462
x17 = 106.226147618505
x18 = 65.3854431218381
x19 = 45.8748440314486
x20 = -10.0127805643169
x21 = -95.496825380092
x22 = 33.9695165859402
x23 = -22.5791511786761
x24 = -64.0808988441941
x25 = 5.03413953478133
x26 = 77.9518137361973
x27 = -38.2871144466251
x28 = 92.9987338352955
x29 = -44.5702997538047
x30 = 27.0252881099099
x31 = 5.69518270363202
x32 = 96.1403264888853
x33 = 8.17573218837112
x34 = 52.1580293386282
x35 = 43.3942945467095
x36 = -69.703040982523
x37 = 64.7243999529874
x38 = -97.9773748648312
x39 = -91.6941895576516
x40 = 71.007585260167
x41 = 23.8836954563201
x42 = -23.2401943475268
x43 = 62.2438504682483
x44 = 87.3765916969666
x45 = -346.163194498425
x46 = -89.2136400729125
x47 = -29.5233796547064
x48 = 80.4323632209364
x49 = -32.0039291394455
x50 = -67.2224914977839
x51 = 36.4500660706793
x52 = -1.24904577239825
x53 = 18.2615533179912
x54 = -0.588002603547568
x55 = 99.9429623113258
x56 = -53.9950777145741
x57 = -7.53223107957784
x58 = -45.2313429226554
x59 = 67.8659926065772
x60 = 11.9783680108116
x61 = -82.2694115968822
x62 = 30.1668807634997
x63 = -57.7977135370145
x64 = 84.2349990433768
x65 = -35.806564961886
x66 = 42.7332513778588
x67 = 14.4589174955507
x68 = -60.2782630217536
x69 = -47.7118924073945
x70 = 1.89254688119154
x71 = 27.6863312787606
x72 = 40.2527018931197
x73 = 58.4412146458078
x74 = 74.1491779137568
x75 = 39.5916587242691
x76 = -66.5614483289332
x77 = -88.5525969040618
x78 = -73.5056768049635
x79 = 21.403145971581
x80 = -25.7207438322659
x81 = -16.2959658714965
x82 = -20.098601693937
x82 = -20.098601693937
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