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4sin^2x-2sinxcosx=3 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
     2                         
4*sin (x) - 2*sin(x)*cos(x) = 3
$$4 \sin^{2}{\left(x \right)} - 2 \sin{\left(x \right)} \cos{\left(x \right)} = 3$$
Simplificar
Gráfica
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
     -pi 
x1 = ----
      4
$$x_{1} = - \frac{\pi}{4}$$ 
     3*pi
x2 = ----
      4
$$x_{2} = \frac{3 \pi}{4}$$ 
            /      ____\
            |1   \/ 10 |
x3 = -2*atan|- - ------|
            \3     3   /
$$x_{3} = - 2 \operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{10}}{3} \right)}$$ 
            /      ____\
            |1   \/ 10 |
x4 = -2*atan|- + ------|
            \3     3   /
$$x_{4} = - 2 \operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{10}}{3} \right)}$$ 
x4 = -2*atan(1/3 + sqrt(10)/3)
Suma y producto de raíces [src] 
suma
                    /      ____\         /      ____\
  pi   3*pi         |1   \/ 10 |         |1   \/ 10 |
- -- + ---- - 2*atan|- - ------| - 2*atan|- + ------|
  4     4           \3     3   /         \3     3   /
$$- 2 \operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{10}}{3} \right)} + \left(- 2 \operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{10}}{3} \right)} + \left(- \frac{\pi}{4} + \frac{3 \pi}{4}\right)\right)$$ 
=
           /      ____\         /      ____\
pi         |1   \/ 10 |         |1   \/ 10 |
-- - 2*atan|- - ------| - 2*atan|- + ------|
2          \3     3   /         \3     3   /
$$- 2 \operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{10}}{3} \right)} - 2 \operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{10}}{3} \right)} + \frac{\pi}{2}$$ 
producto
                 /      ____\        /      ____\
-pi  3*pi        |1   \/ 10 |        |1   \/ 10 |
----*----*-2*atan|- - ------|*-2*atan|- + ------|
 4    4          \3     3   /        \3     3   /
$$- \frac{\pi}{4} \frac{3 \pi}{4} \left(- 2 \operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{10}}{3} \right)}\right) \left(- 2 \operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{10}}{3} \right)}\right)$$ 
=
           /      ____\     /      ____\
     2     |1   \/ 10 |     |1   \/ 10 |
-3*pi *atan|- - ------|*atan|- + ------|
           \3     3   /     \3     3   /
----------------------------------------
                   4
$$- \frac{3 \pi^{2} \operatorname{atan}{\left(\frac{1}{3} - \frac{\sqrt{10}}{3} \right)} \operatorname{atan}{\left(\frac{1}{3} + \frac{\sqrt{10}}{3} \right)}}{4}$$ 
-3*pi^2*atan(1/3 - sqrt(10)/3)*atan(1/3 + sqrt(10)/3)/4
Respuesta numérica [src] 
x1 = 54.6561208834247
x2 = -41.6261026600648
x3 = -99.2819191424751
x4 = -74.1491779137568
x5 = 18.0641577581413
x6 = -45.8748440314486
x7 = 40.0553063332699
x8 = -47.9092879672443
x9 = 4.39063842598805
x10 = 57.7977135370145
x11 = 96.6039740978861
x12 = 76.6472694585533
x13 = 13.8154163867574
x14 = -16.4933614313464
x15 = -3.92699081698724
x16 = -39.5916587242691
x17 = -8.17573218837112
x18 = -1.89254688119154
x19 = -63.6172512351933
x20 = 55.7632696012188
x21 = 48.3729355762452
x22 = 93.4623814442964
x23 = -10.2101761241668
x24 = 71.4712328691678
x25 = -66.7588438887831
x26 = -17.6005101491405
x27 = -52.1580293386282
x28 = -85.6083998103219
x29 = 33.7721210260903
x30 = -32.2013246992954
x31 = -82.4668071567321
x32 = 2.35619449019234
x33 = 92.3552327265023
x34 = -61.5828072993976
x35 = 10.6738237331676
x36 = -98.174770424681
x37 = 46.3384916404494
x38 = -0.785398163397448
x39 = 5.49778714378214
x40 = 99.7455667514759
x41 = 35.806564961886
x42 = 121.736715326604
x43 = 86.0720474193227
x44 = -91.8915851175014
x45 = -55.299621992218
x46 = 79.7888621121431
x47 = 855.762247548822
x48 = -19.6349540849362
x49 = -60.4756585816035
x50 = 27.4889357189107
x51 = -33.3084734170895
x52 = 84.037603483527
x53 = 64.0808988441941
x54 = -76.1836218495525
x55 = 42.0897502690656
x56 = -77.2907705673466
x57 = -38.484510006475
x58 = -89.8571411817058
x59 = -14.4589174955507
x60 = 68.329640215578
x61 = 70.3640841513737
x62 = 62.0464549083984
x63 = -25.9181393921158
x64 = -67.8659926065772
x65 = 20.098601693937
x66 = 1141.64717902549
x67 = 90.3207887907066
x68 = 11.7809724509617
x69 = 98.6384180336818
x70 = 74.6128255227576
x71 = -54.1924732744239
x72 = -30.1668807634997
x73 = -11.3173248419609
x74 = 26.3817870011166
x75 = -242.688032489812
x76 = -83.5739558745262
x77 = -69.9004365423729
x78 = 49.4800842940392
x79 = -23.8836954563201
x80 = 24.3473430653209
x81 = -96.1403264888853
x82 = 32.6649723082962
x83 = -95.0331777710912
x84 = 77.7544181763474
x84 = 77.7544181763474
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