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4sin^2(x)+5sinxcosx-6cos^2(x)=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
     2                             2       
4*sin (x) + 5*sin(x)*cos(x) - 6*cos (x) = 0
$$\left(4 \sin^{2}{\left(x \right)} + 5 \sin{\left(x \right)} \cos{\left(x \right)}\right) - 6 \cos^{2}{\left(x \right)} = 0$$
Simplificar
Gráfica
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
x1 = 2*atan(1/3)
$$x_{1} = 2 \operatorname{atan}{\left(\frac{1}{3} \right)}$$ 
x2 = -2*atan(3)
$$x_{2} = - 2 \operatorname{atan}{\left(3 \right)}$$ 
           /      ___\
           |1   \/ 5 |
x3 = 2*atan|- - -----|
           \2     2  /
$$x_{3} = 2 \operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{5}}{2} \right)}$$ 
           /      ___\
           |1   \/ 5 |
x4 = 2*atan|- + -----|
           \2     2  /
$$x_{4} = 2 \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)}$$ 
x4 = 2*atan(1/2 + sqrt(5)/2)
Suma y producto de raíces [src] 
suma
                                /      ___\         /      ___\
                                |1   \/ 5 |         |1   \/ 5 |
2*atan(1/3) - 2*atan(3) + 2*atan|- - -----| + 2*atan|- + -----|
                                \2     2  /         \2     2  /
$$\left(\left(- 2 \operatorname{atan}{\left(3 \right)} + 2 \operatorname{atan}{\left(\frac{1}{3} \right)}\right) + 2 \operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{5}}{2} \right)}\right) + 2 \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)}$$ 
=
                                 /      ___\         /      ___\
                                 |1   \/ 5 |         |1   \/ 5 |
-2*atan(3) + 2*atan(1/3) + 2*atan|- + -----| + 2*atan|- - -----|
                                 \2     2  /         \2     2  /
$$- 2 \operatorname{atan}{\left(3 \right)} + 2 \operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{5}}{2} \right)} + 2 \operatorname{atan}{\left(\frac{1}{3} \right)} + 2 \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)}$$ 
producto
                             /      ___\       /      ___\
                             |1   \/ 5 |       |1   \/ 5 |
2*atan(1/3)*-2*atan(3)*2*atan|- - -----|*2*atan|- + -----|
                             \2     2  /       \2     2  /
$$2 \operatorname{atan}{\left(\frac{1}{3} \right)} \left(- 2 \operatorname{atan}{\left(3 \right)}\right) 2 \operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{5}}{2} \right)} 2 \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)}$$ 
=
                          /      ___\     /      ___\
                          |1   \/ 5 |     |1   \/ 5 |
-16*atan(3)*atan(1/3)*atan|- + -----|*atan|- - -----|
                          \2     2  /     \2     2  /
$$- 16 \operatorname{atan}{\left(\frac{1}{3} \right)} \operatorname{atan}{\left(3 \right)} \operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{5}}{2} \right)} \operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)}$$ 
-16*atan(3)*atan(1/3)*atan(1/2 + sqrt(5)/2)*atan(1/2 - sqrt(5)/2)
Respuesta numérica [src] 
x1 = 60.3337615269994
x2 = 36.5919631252834
x3 = -35.6646679072818
x4 = 47.7673909126402
x5 = 88.6080954093075
x6 = -57.6558164824104
x7 = -112.453834420439
x8 = 33.4503704716936
x9 = -77.8963152309515
x10 = -11.9228695055659
x11 = -51.3726311752308
x12 = -55.905166655823
x13 = -54.5142238288206
x14 = 30.3087778181038
x15 = -70.2221870967695
x16 = -76.5053724039491
x17 = 25.7762423375116
x18 = -27.6308327735149
x19 = 98.0328733700769
x20 = -98.4965209790777
x21 = 66.6169468341789
x22 = -99.8874638060801
x23 = 3.78509376238308
x24 = 120.024021945205
x25 = 83.7158529291303
x26 = -3742.74399914324
x27 = 22.6346496839218
x28 = 10.0682790695627
x29 = -43.3387960414638
x30 = 99.4238161970793
x31 = 69.7585394877687
x32 = -63.93900178959
x33 = 77.4326676219507
x34 = -49.6219813486434
x35 = -90.4626858453107
x36 = -87.3210931917209
x37 = 52.2999263932324
x38 = -19.9567046393328
x39 = -4.24874137138388
x40 = 39.7335557788732
x41 = 14.6008145501549
x42 = -95.3549283254879
x43 = 0.643501108793284
x44 = -71.613129923772
x45 = -84.1795005381311
x46 = 76.0417247949483
x47 = 96.2822235434895
x48 = -41.9478532144614
x49 = 8.31762924297529
x50 = 16.3514643767422
x51 = -33.9140180806944
x52 = -93.6042784989005
x53 = 80.5742602755405
x54 = 89.9990382363099
x55 = 2.0344439357957
x56 = 17.7424072037447
x57 = 82.3249101021279
x58 = -85.9301503647185
x59 = 46.0167410860528
x60 = -92.2133356718981
x61 = -73.3637797503593
x62 = -40.197203387874
x63 = -13.6735193321533
x64 = 74.2910749683609
x65 = -62.1883519630026
x66 = -5.6396841983863
x67 = 44.6257982590504
x68 = -32.523075253692
x69 = -18.2060548127455
x70 = 58.583111700412
x71 = 38.3426129518708
x72 = -65.3299446165924
x73 = 55.4415190468222
x74 = -29.3814826001022
x75 = 24.0255925109243
x76 = 61.7247043540018
x77 = -10.5319266785635
x78 = -26.2398899465124
x79 = 32.0594276446912
x80 = 54.0505762198198
x81 = 68.0078896611814
x82 = 91.7496880628973
x83 = 123.165614598795
x84 = 11.4592218965651
x85 = -7.39033402497368
x86 = -79.6469650575389
x87 = -48.231038521641
x88 = -21.3476474663353
x88 = -21.3476474663353
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