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sin2x+4((cosx)^2)=1 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
                2       
sin(2*x) + 4*cos (x) = 1
$$\sin{\left(2 x \right)} + 4 \cos^{2}{\left(x \right)} = 1$$
Simplificar
Gráfica
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
  pi           /log(10)      /  ____\\               /log(10)      /  ____\\                  /    5/2\
- -- + -pi + I*|------- - log\\/ 10 /| + atan(3) + I*|------- - log\\/ 10 /| + atan(3) - I*log\(-I)   /
  4            \   2                 /               \   2                 /
$$- i \log{\left(\left(- i\right)^{\frac{5}{2}} \right)} + \left(\left(- \frac{\pi}{4} + \left(- \pi + \operatorname{atan}{\left(3 \right)} + i \left(- \log{\left(\sqrt{10} \right)} + \frac{\log{\left(10 \right)}}{2}\right)\right)\right) + \left(\operatorname{atan}{\left(3 \right)} + i \left(- \log{\left(\sqrt{10} \right)} + \frac{\log{\left(10 \right)}}{2}\right)\right)\right)$$ 
=
            5*pi        /    5/2\       /log(10)      /  ____\\
2*atan(3) - ---- - I*log\(-I)   / + 2*I*|------- - log\\/ 10 /|
             4                          \   2                 /
$$- \frac{5 \pi}{4} - i \log{\left(\left(- i\right)^{\frac{5}{2}} \right)} + 2 \operatorname{atan}{\left(3 \right)} + 2 i \left(- \log{\left(\sqrt{10} \right)} + \frac{\log{\left(10 \right)}}{2}\right)$$ 
producto
-pi  /        /log(10)      /  ____\\          \ /  /log(10)      /  ____\\          \ /      /    5/2\\
----*|-pi + I*|------- - log\\/ 10 /| + atan(3)|*|I*|------- - log\\/ 10 /| + atan(3)|*\-I*log\(-I)   //
 4   \        \   2                 /          / \  \   2                 /          /
$$- i \log{\left(\left(- i\right)^{\frac{5}{2}} \right)} - \frac{\pi}{4} \left(- \pi + \operatorname{atan}{\left(3 \right)} + i \left(- \log{\left(\sqrt{10} \right)} + \frac{\log{\left(10 \right)}}{2}\right)\right) \left(\operatorname{atan}{\left(3 \right)} + i \left(- \log{\left(\sqrt{10} \right)} + \frac{\log{\left(10 \right)}}{2}\right)\right)$$ 
=
                                /    5/2\
pi*I*(-pi + atan(3))*atan(3)*log\(-I)   /
-----------------------------------------
                    4
$$\frac{i \pi \left(- \pi + \operatorname{atan}{\left(3 \right)}\right) \log{\left(\left(- i\right)^{\frac{5}{2}} \right)} \operatorname{atan}{\left(3 \right)}}{4}$$ 
pi*i*(-pi + atan(3))*atan(3)*log((-i)^(5/2))/4
Respuesta rápida [src] 
     -pi 
x1 = ----
      4
$$x_{1} = - \frac{\pi}{4}$$ 
             /log(10)      /  ____\\          
x2 = -pi + I*|------- - log\\/ 10 /| + atan(3)
             \   2                 /
$$x_{2} = - \pi + \operatorname{atan}{\left(3 \right)} + i \left(- \log{\left(\sqrt{10} \right)} + \frac{\log{\left(10 \right)}}{2}\right)$$ 
       /log(10)      /  ____\\          
x3 = I*|------- - log\\/ 10 /| + atan(3)
       \   2                 /
$$x_{3} = \operatorname{atan}{\left(3 \right)} + i \left(- \log{\left(\sqrt{10} \right)} + \frac{\log{\left(10 \right)}}{2}\right)$$ 
           /    5/2\
x4 = -I*log\(-I)   /
$$x_{4} = - i \log{\left(\left(- i\right)^{\frac{5}{2}} \right)}$$ 
x4 = -i*log((-i)^(5/2))
Respuesta numérica [src] 
x1 = -33.3084734170895
x2 = 96.6039740978861
x3 = 68.329640215578
x4 = -45.8748440314486
x5 = -91.8915851175014
x6 = -77.2907705673466
x7 = 99.7455667514759
x8 = -23.8836954563201
x9 = -3.92699081698724
x10 = -54.1924732744239
x11 = -61.5828072993976
x12 = -10.2101761241668
x13 = -16.4933614313464
x14 = -76.1836218495525
x15 = -25.9181393921158
x16 = -74.1491779137568
x17 = 98.6384180336818
x18 = -1449.05961146829
x19 = -89.8571411817058
x20 = 77.7544181763474
x21 = -17.6005101491405
x22 = -11.3173248419609
x23 = -55.299621992218
x24 = 27.4889357189107
x25 = 71.4712328691678
x26 = -8.17573218837112
x27 = -14.4589174955507
x28 = 93.4623814442964
x29 = -66.7588438887831
x30 = -52.1580293386282
x31 = -69.9004365423729
x32 = 20.098601693937
x33 = -82.4668071567321
x34 = 2.35619449019234
x35 = -19.6349540849362
x36 = 24.3473430653209
x37 = -30.1668807634997
x38 = 70.3640841513737
x39 = 64.0808988441941
x40 = -85.6083998103219
x41 = 86.0720474193227
x42 = 90.3207887907066
x43 = -96.1403264888853
x44 = 74.6128255227576
x45 = 40.0553063332699
x46 = -99.2819191424751
x47 = 57.7977135370145
x48 = 13.8154163867574
x49 = -98.174770424681
x50 = 26.3817870011166
x51 = 35.806564961886
x52 = 48.3729355762452
x53 = 76.6472694585533
x54 = 84.037603483527
x55 = -63.6172512351933
x56 = -242.688032489812
x57 = 33.7721210260903
x58 = 32.6649723082962
x59 = 168.860605130451
x60 = 46.3384916404494
x61 = -32.2013246992954
x62 = 11.7809724509617
x63 = -41.6261026600648
x64 = -1.89254688119154
x65 = 79.7888621121431
x66 = 42.0897502690656
x67 = -38.484510006475
x68 = -67.8659926065772
x69 = 18.0641577581413
x70 = -60.4756585816035
x71 = -47.9092879672443
x72 = 4.39063842598805
x73 = 55.7632696012188
x74 = 62.0464549083984
x75 = 49.4800842940392
x76 = 54.6561208834247
x77 = -0.785398163397448
x78 = -83.5739558745262
x79 = 92.3552327265023
x80 = -95.0331777710912
x81 = 5.49778714378214
x82 = 10.6738237331676
x83 = -39.5916587242691
x83 = -39.5916587242691
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