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(2*sin(x)+sqrt(2))(2*cos(x)-1)=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
/             ___\                   
\2*sin(x) + \/ 2 /*(2*cos(x) - 1) = 0
$$\left(2 \sin{\left(x \right)} + \sqrt{2}\right) \left(2 \cos{\left(x \right)} - 1\right) = 0$$
Gráfica
Suma y producto de raíces [src]
suma
  3*pi   pi   pi   pi
- ---- - -- - -- + --
   4     3    4    3 
$$\left(\left(- \frac{3 \pi}{4} - \frac{\pi}{3}\right) - \frac{\pi}{4}\right) + \frac{\pi}{3}$$
=
-pi
$$- \pi$$
producto
-3*pi -pi  -pi  pi
-----*----*----*--
  4    3    4   3 
$$\frac{\pi}{3} \cdot - \frac{\pi}{4} \cdot - \frac{3 \pi}{4} \left(- \frac{\pi}{3}\right)$$
=
   4 
-pi  
-----
  48 
$$- \frac{\pi^{4}}{48}$$
-pi^4/48
Respuesta rápida [src]
     -3*pi
x1 = -----
       4  
$$x_{1} = - \frac{3 \pi}{4}$$
     -pi 
x2 = ----
      3  
$$x_{2} = - \frac{\pi}{3}$$
     -pi 
x3 = ----
      4  
$$x_{3} = - \frac{\pi}{4}$$
     pi
x4 = --
     3 
$$x_{4} = \frac{\pi}{3}$$
x4 = pi/3
Respuesta numérica [src]
x1 = -13.6135681655558
x2 = -0.785398163397448
x3 = -38.484510006475
x4 = -40.0553063332699
x5 = 80.8960108299372
x6 = -57.5958653158129
x7 = -36.6519142918809
x8 = 85.6083998103219
x9 = 54.1924732744239
x10 = 76.4454212373516
x11 = 36.9137136796801
x12 = 11.7809724509617
x13 = 63.8790506229925
x14 = -24.0855436775217
x15 = -1.0471975511966
x16 = 95.2949771588904
x17 = 42.9350995990605
x18 = 1262.1348485797
x19 = 80.634211442138
x20 = 70.162235930172
x21 = -19.8967534727354
x22 = -86.9173967493176
x23 = -38.7463093942741
x24 = -88.7499924639117
x25 = 73.0420291959627
x26 = -80.634211442138
x27 = 86.9173967493176
x28 = -84.037603483527
x29 = 26.1799387799149
x30 = -69.9004365423729
x31 = 49.4800842940392
x32 = -27.4889357189107
x33 = 7.33038285837618
x34 = 57.5958653158129
x35 = -76.1836218495525
x36 = 62.0464549083984
x37 = -32.2013246992954
x38 = -68.0678408277789
x39 = -65.1880475619882
x40 = 1463.19677840945
x41 = -77.7544181763474
x42 = 47.9092879672443
x43 = 93.4623814442964
x44 = 91.8915851175014
x45 = -74.3510261349584
x46 = -44.7676953136546
x47 = -58.9048622548086
x48 = 99.7455667514759
x49 = 66.7588438887831
x50 = -63.8790506229925
x51 = 24.0855436775217
x52 = -21.2057504117311
x53 = -7.33038285837618
x54 = 98.174770424681
x55 = 10.2101761241668
x56 = 32.4631240870945
x57 = 19.8967534727354
x58 = -95.2949771588904
x59 = 74.3510261349584
x60 = 55.7632696012188
x61 = 51.3126800086333
x62 = 22.776546738526
x63 = -61.7846555205993
x64 = -14.9225651045515
x65 = 60.4756585816035
x66 = -51.0508806208341
x67 = -17.8023583703422
x68 = -33.7721210260903
x69 = -71.4712328691678
x70 = 36.6519142918809
x71 = 3.92699081698724
x72 = 18.0641577581413
x73 = -99.4837673636768
x74 = 30.3687289847013
x75 = 68.0678408277789
x76 = 87.1791961371168
x77 = -55.5014702134197
x78 = -82.4668071567321
x79 = -11.5191730631626
x80 = -51.3126800086333
x81 = 13.6135681655558
x82 = -30.3687289847013
x83 = 11.5191730631626
x84 = -107.59954838545
x85 = 29.0597320457056
x86 = 5.49778714378214
x87 = -25.9181393921158
x88 = 16.4933614313464
x88 = 16.4933614313464