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

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Solución numérica:

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Solución

Ha introducido [src]
     2                         2       
6*sin (x) + sin(x)*cos(x) - cos (x) = 2
$$\left(6 \sin^{2}{\left(x \right)} + \sin{\left(x \right)} \cos{\left(x \right)}\right) - \cos^{2}{\left(x \right)} = 2$$
Gráfica
Respuesta rápida [src]
     -pi 
x1 = ----
      4  
$$x_{1} = - \frac{\pi}{4}$$
     3*pi
x2 = ----
      4  
$$x_{2} = \frac{3 \pi}{4}$$
x3 = 2*atan(1/3)
$$x_{3} = 2 \operatorname{atan}{\left(\frac{1}{3} \right)}$$
x4 = -2*atan(3)
$$x_{4} = - 2 \operatorname{atan}{\left(3 \right)}$$
x4 = -2*atan(3)
Suma y producto de raíces [src]
suma
  pi   3*pi                          
- -- + ---- + 2*atan(1/3) - 2*atan(3)
  4     4                            
$$- 2 \operatorname{atan}{\left(3 \right)} + \left(2 \operatorname{atan}{\left(\frac{1}{3} \right)} + \left(- \frac{\pi}{4} + \frac{3 \pi}{4}\right)\right)$$
=
pi                          
-- - 2*atan(3) + 2*atan(1/3)
2                           
$$- 2 \operatorname{atan}{\left(3 \right)} + 2 \operatorname{atan}{\left(\frac{1}{3} \right)} + \frac{\pi}{2}$$
producto
-pi  3*pi                       
----*----*2*atan(1/3)*-2*atan(3)
 4    4                         
$$- \frac{\pi}{4} \frac{3 \pi}{4} \cdot 2 \operatorname{atan}{\left(\frac{1}{3} \right)} \left(- 2 \operatorname{atan}{\left(3 \right)}\right)$$
=
    2                  
3*pi *atan(3)*atan(1/3)
-----------------------
           4           
$$\frac{3 \pi^{2} \operatorname{atan}{\left(\frac{1}{3} \right)} \operatorname{atan}{\left(3 \right)}}{4}$$
3*pi^2*atan(3)*atan(1/3)/4
Respuesta numérica [src]
x1 = 47.7673909126402
x2 = -27.6308327735149
x3 = -57.3340659280137
x4 = 93.4623814442964
x5 = -79.3252145031423
x6 = 74.6128255227576
x7 = -99.8874638060801
x8 = -54.1924732744239
x9 = 98.0328733700769
x10 = 18.0641577581413
x11 = 46.3384916404494
x12 = 60.3337615269994
x13 = -76.1836218495525
x14 = 32.0594276446912
x15 = -93.6042784989005
x16 = -87.3210931917209
x17 = 55.7632696012188
x18 = -40.197203387874
x19 = 2.35619449019234
x20 = -21.3476474663353
x21 = 69.7585394877687
x22 = 84.037603483527
x23 = 33.7721210260903
x24 = 3.78509376238308
x25 = -85.6083998103219
x26 = -71.613129923772
x27 = 19.493057030332
x28 = 4757.01477864374
x29 = 76.0417247949483
x30 = 66.6169468341789
x31 = 8.63937979737193
x32 = -19.6349540849362
x33 = -33.9140180806944
x34 = -2.49809154479651
x35 = -55.905166655823
x36 = -46.4803886950536
x37 = -18.2060548127455
x38 = 16.3514643767422
x39 = -69.9004365423729
x40 = 82.3249101021279
x41 = -13.3517687777566
x42 = -32.2013246992954
x43 = 96.6039740978861
x44 = 22.6346496839218
x45 = -35.3429173528852
x46 = -24.4892401199251
x47 = -90.4626858453107
x48 = -10.2101761241668
x49 = 21.2057504117311
x50 = -84.1795005381311
x51 = -82.4668071567321
x52 = -43.3387960414638
x53 = -60.4756585816035
x54 = 91.7496880628973
x55 = 11.7809724509617
x56 = 90.3207887907066
x57 = -25.9181393921158
x58 = 68.329640215578
x59 = 0.643501108793284
x60 = -3987.46647556884
x61 = -98.174770424681
x62 = -41.6261026600648
x63 = -47.9092879672443
x64 = -68.4715372701822
x65 = -11.9228695055659
x66 = 63.4753541805892
x67 = 24.3473430653209
x68 = -91.8915851175014
x69 = 40.0553063332699
x70 = 38.3426129518708
x71 = 30.6305283725005
x72 = 462.457621186493
x73 = -5.6396841983863
x74 = -63.6172512351933
x75 = 85.4665027557177
x76 = 52.621676947629
x77 = -62.1883519630026
x78 = 10.0682790695627
x79 = -77.8963152309515
x80 = -3.92699081698724
x81 = 41.4842056054606
x82 = 54.0505762198198
x83 = 77.7544181763474
x84 = -65.3299446165924
x85 = 88.6080954093075
x86 = 62.0464549083984
x87 = 44.6257982590504
x88 = 99.7455667514759
x89 = -49.6219813486434
x90 = 25.7762423375116
x90 = 25.7762423375116