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6sin^2x+sin2x=2 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
     2                  
6*sin (x) + sin(2*x) = 2
$$6 \sin^{2}{\left(x \right)} + \sin{\left(2 x \right)} = 2$$
Gráfica
Respuesta rápida [src]
     -pi 
x1 = ----
      4  
$$x_{1} = - \frac{\pi}{4}$$
             /log(5)      /  ___\\            
x2 = -pi + I*|------ - log\\/ 5 /| + atan(1/2)
             \  2                /            
$$x_{2} = - \pi + \operatorname{atan}{\left(\frac{1}{2} \right)} + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)$$
       /log(5)      /  ___\\            
x3 = I*|------ - log\\/ 5 /| + atan(1/2)
       \  2                /            
$$x_{3} = \operatorname{atan}{\left(\frac{1}{2} \right)} + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)$$
           /    5/2\
x4 = -I*log\(-I)   /
$$x_{4} = - i \log{\left(\left(- i\right)^{\frac{5}{2}} \right)}$$
x4 = -i*log((-i)^(5/2))
Suma y producto de raíces [src]
suma
  pi           /log(5)      /  ___\\                 /log(5)      /  ___\\                    /    5/2\
- -- + -pi + I*|------ - log\\/ 5 /| + atan(1/2) + I*|------ - log\\/ 5 /| + atan(1/2) - I*log\(-I)   /
  4            \  2                /                 \  2                /                             
$$- i \log{\left(\left(- i\right)^{\frac{5}{2}} \right)} + \left(\left(- \frac{\pi}{4} + \left(- \pi + \operatorname{atan}{\left(\frac{1}{2} \right)} + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)\right)\right) + \left(\operatorname{atan}{\left(\frac{1}{2} \right)} + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)\right)\right)$$
=
              5*pi        /    5/2\       /log(5)      /  ___\\
2*atan(1/2) - ---- - I*log\(-I)   / + 2*I*|------ - log\\/ 5 /|
               4                          \  2                /
$$- \frac{5 \pi}{4} + 2 \operatorname{atan}{\left(\frac{1}{2} \right)} - i \log{\left(\left(- i\right)^{\frac{5}{2}} \right)} + 2 i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)$$
producto
-pi  /        /log(5)      /  ___\\            \ /  /log(5)      /  ___\\            \ /      /    5/2\\
----*|-pi + I*|------ - log\\/ 5 /| + atan(1/2)|*|I*|------ - log\\/ 5 /| + atan(1/2)|*\-I*log\(-I)   //
 4   \        \  2                /            / \  \  2                /            /                  
$$- i \log{\left(\left(- i\right)^{\frac{5}{2}} \right)} - \frac{\pi}{4} \left(- \pi + \operatorname{atan}{\left(\frac{1}{2} \right)} + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)\right) \left(\operatorname{atan}{\left(\frac{1}{2} \right)} + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)\right)$$
=
                                    /    5/2\
pi*I*(-pi + atan(1/2))*atan(1/2)*log\(-I)   /
---------------------------------------------
                      4                      
$$\frac{i \pi \left(- \pi + \operatorname{atan}{\left(\frac{1}{2} \right)}\right) \log{\left(\left(- i\right)^{\frac{5}{2}} \right)} \operatorname{atan}{\left(\frac{1}{2} \right)}}{4}$$
pi*i*(-pi + atan(1/2))*atan(1/2)*log((-i)^(5/2))/4
Respuesta numérica [src]
x1 = 9.88842556977019
x2 = 88.428241909515
x3 = 25.5963888377192
x4 = 44.4459447592579
x5 = 30.6305283725005
x6 = 84.037603483527
x7 = -56.0850201556155
x8 = 0.463647609000806
x9 = 1486.43697275697
x10 = 11.7809724509617
x11 = 68.329640215578
x12 = 16.1716108769498
x13 = -49.8018348484359
x14 = -54.1924732744239
x15 = -93.784131998693
x16 = -47.9092879672443
x17 = -71.7929834235644
x18 = 90.3207887907066
x19 = -126.449104306989
x20 = 8.63937979737193
x21 = -69.9004365423729
x22 = -19.6349540849362
x23 = 75.8618712951559
x24 = -40.3770568876665
x25 = -3.92699081698724
x26 = -76.1836218495525
x27 = 62.0464549083984
x28 = 38.1627594520783
x29 = -32.2013246992954
x30 = 3.6052402625906
x31 = 91.5698345631048
x32 = -84.3593540379236
x33 = -43.5186495412563
x34 = 82.1450566023354
x35 = -5.81953769817878
x36 = 47.5875374128477
x37 = 31.8795741448987
x38 = -78.076168730744
x39 = -18.385908312538
x40 = 24.3473430653209
x41 = 97.8530198702844
x42 = -66.7588438887831
x43 = 99.7455667514759
x44 = 40.0553063332699
x45 = -13.3517687777566
x46 = -34.0938715804869
x47 = -87.5009466915134
x48 = 22.4547961841294
x49 = -12.1027230053584
x50 = 66.4370933343865
x51 = 55.7632696012188
x52 = -79.3252145031423
x53 = -100.067317305873
x54 = 69.5786859879763
x55 = -21.5275009661277
x56 = 159.435827169682
x57 = 74.6128255227576
x58 = -62.3682054627951
x59 = 18.0641577581413
x60 = -41.6261026600648
x61 = -85.6083998103219
x62 = -35.3429173528852
x63 = 53.8707227200273
x64 = 52.621676947629
x65 = 60.1539080272069
x66 = 96.6039740978861
x67 = -63.6172512351933
x68 = -10.2101761241668
x69 = 46.3384916404494
x70 = -27.8106862733073
x71 = -91.8915851175014
x72 = -98.174770424681
x73 = -57.3340659280137
x74 = -65.5097981163849
x75 = 77.7544181763474
x76 = -25.9181393921158
x77 = 2.35619449019234
x78 = 33.7721210260903
x78 = 33.7721210260903