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

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
                  ___            ___               
                \/ 2           \/ 2           1    
cos(x)*sin(x) + -----*cos(x) - -----*sin(x) - - = 0
                  2              2            2    
$$\left(\left(\sin{\left(x \right)} \cos{\left(x \right)} + \frac{\sqrt{2}}{2} \cos{\left(x \right)}\right) - \frac{\sqrt{2}}{2} \sin{\left(x \right)}\right) - \frac{1}{2} = 0$$
Gráfica
Respuesta rápida [src]
     -3*pi
x1 = -----
       4  
$$x_{1} = - \frac{3 \pi}{4}$$
     -pi 
x2 = ----
      4  
$$x_{2} = - \frac{\pi}{4}$$
     pi
x3 = --
     4 
$$x_{3} = \frac{\pi}{4}$$
x3 = pi/4
Suma y producto de raíces [src]
suma
  3*pi   pi   pi
- ---- - -- + --
   4     4    4 
$$\left(- \frac{3 \pi}{4} - \frac{\pi}{4}\right) + \frac{\pi}{4}$$
=
-3*pi
-----
  4  
$$- \frac{3 \pi}{4}$$
producto
-3*pi -pi  pi
-----*----*--
  4    4   4 
$$\frac{\pi}{4} \cdot - \frac{3 \pi}{4} \left(- \frac{\pi}{4}\right)$$
=
    3
3*pi 
-----
  64 
$$\frac{3 \pi^{3}}{64}$$
3*pi^3/64
Respuesta numérica [src]
x1 = 25.9181393921158
x2 = 87.1791957824773
x3 = -36.9137136796801
x4 = -25.918140046808
x5 = -7.06858278595795
x6 = -0.785398387140928
x7 = -44.7676957361531
x8 = 99.745566900108
x9 = -99.7455667514759
x10 = 22.776546738526
x11 = -90.3207887907066
x12 = -65.1880475619882
x13 = -38.484509820882
x14 = 82.4668071567321
x15 = 38.484510006475
x16 = 7.06858347057703
x17 = -76.1836217282209
x18 = -77.7544181763474
x19 = 24.3473430048829
x20 = -5.49778714378214
x21 = 73.0420291959627
x22 = -7.06858351214916
x23 = 76.1836218495525
x24 = 54.1924732744239
x25 = -88.7499927410741
x26 = -62.0464549083984
x27 = 91.8915851175014
x28 = 51.0508806208341
x29 = 63.6172512351933
x30 = -0.785398070020699
x31 = -33.7721210260903
x32 = -44.7676949864154
x33 = 10.2101761241668
x34 = 30.6305273736884
x35 = -82.4668069702928
x36 = -32.2013245705094
x37 = 5.49778732761904
x38 = -30.6305283725005
x39 = 11.7809725867768
x40 = 74.6128253583021
x41 = -51.0508806134381
x42 = 49.4800844750815
x43 = -63.6172513138819
x44 = -19.6349541546828
x45 = 87.179194571984
x46 = 62.0464548193084
x47 = -40.0553063332699
x48 = 43.196898824959
x49 = 49.480084433185
x50 = 98.174770424681
x51 = -14.9225651045515
x52 = 80.896010725149
x53 = -24.3473430653209
x54 = 29.0597320457056
x55 = 16.4933614313464
x56 = 3.92699081698724
x57 = -80.8960108299372
x58 = -46.3384916404494
x59 = -95.0331780630375
x60 = -95.0331776963524
x61 = -57.3340661026433
x62 = 55.763269743648
x63 = -93.4623814442964
x64 = -74.6128255227576
x65 = -55.7632696012188
x66 = -27.4889357189107
x67 = -84.037603483527
x68 = 531.714556620072
x69 = 68.3296401648505
x70 = -51.050879648505
x71 = 95.0331777710912
x72 = -11.7809724509617
x73 = 43.196900220913
x74 = -76.1836207058187
x75 = 55.7632696992475
x76 = -71.4712328691678
x77 = -13.3517689495277
x78 = 79.3252145031423
x79 = 93.4623816213382
x80 = 32.2013246992954
x81 = -49.4800842940392
x82 = 13.3517687777566
x83 = 57.3340659280137
x84 = 30.6305282041351
x85 = 36.9137133992238
x86 = 36.9137136019555
x87 = -88.7499919932625
x88 = 18.0641575840826
x89 = 60.4756585816035
x90 = -58.9048622548086
x91 = 47.9092879672443
x92 = 69.9004365423729
x93 = -7.06858433593904
x94 = -68.329640215578
x95 = 66.7588438887831
x96 = 19.6349540849362
x97 = -21.2057504117311
x98 = -18.0641577581413
x98 = -18.0641577581413