Sr Examen

cosx+sinx=(sinx+cosx)² la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
                                   2
cos(x) + sin(x) = (sin(x) + cos(x)) 
$$\sin{\left(x \right)} + \cos{\left(x \right)} = \left(\sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2}$$
Gráfica
Suma y producto de raíces [src]
suma
  pi   pi   3*pi
- -- + -- + ----
  4    2     4  
$$\left(- \frac{\pi}{4} + \frac{\pi}{2}\right) + \frac{3 \pi}{4}$$
=
pi
$$\pi$$
producto
  -pi  pi 3*pi
0*----*--*----
   4   2   4  
$$\frac{3 \pi}{4} \frac{\pi}{2} \cdot 0 \left(- \frac{\pi}{4}\right)$$
=
0
$$0$$
0
Respuesta rápida [src]
x1 = 0
$$x_{1} = 0$$
     -pi 
x2 = ----
      4  
$$x_{2} = - \frac{\pi}{4}$$
     pi
x3 = --
     2 
$$x_{3} = \frac{\pi}{2}$$
     3*pi
x4 = ----
      4  
$$x_{4} = \frac{3 \pi}{4}$$
x4 = 3*pi/4
Respuesta numérica [src]
x1 = 18.0641577581413
x2 = 14.1371669411541
x3 = 33.7721210260903
x4 = -80.1106126665397
x5 = 71.4712328691678
x6 = -51.0508806208341
x7 = -69.9004365423729
x8 = 46.3384916404494
x9 = -6.28318530717959
x10 = 95.8185759344887
x11 = -98.174770424681
x12 = 37.6991118430775
x13 = -66.7588438887831
x14 = 100.530964914873
x15 = 36.9137136796801
x16 = -7.06858347057703
x17 = 94.2477796076938
x18 = 32.9867228626928
x19 = 7.85398163397448
x20 = 30.6305283725005
x21 = -29.845130209103
x22 = -91.8915851175014
x23 = 70.6858347057703
x24 = -88.7499924639117
x25 = -87.9645943005142
x26 = 0.0
x27 = -73.0420291959627
x28 = -17.2787595947439
x29 = -67.5442420521806
x30 = 50.2654824574367
x31 = 65.1880475619882
x32 = -19.6349540849362
x33 = 68.329640215578
x34 = 45.553093477052
x35 = -105.243353895258
x36 = -23.5619449019235
x37 = -57.3340659280137
x38 = 58.1194640914112
x39 = -85.6083998103219
x40 = -4644.05934016911
x41 = -47.9092879672443
x42 = -32.2013246992954
x43 = -44.7676953136546
x44 = 40.0553063332699
x45 = -36.1283155162826
x46 = 87.9645943005142
x47 = -73.8274273593601
x48 = 64.4026493985908
x49 = -69.1150383789755
x50 = 27.4889357189107
x51 = 81.6814089933346
x52 = 24.3473430653209
x53 = -25.9181393921158
x54 = -43.9822971502571
x55 = -37.6991118430775
x56 = -13.3517687777566
x57 = -16.4933614313464
x58 = 20.4203522483337
x59 = 87.1791961371168
x60 = -10.9955742875643
x61 = 6.28318530717959
x62 = 90.3207887907066
x63 = -95.0331777710912
x64 = -3.92699081698724
x65 = -94.2477796076938
x66 = -0.785398163397448
x67 = -29.0597320457056
x68 = 43.9822971502571
x69 = 77.7544181763474
x70 = 31.4159265358979
x71 = -41.6261026600648
x72 = -54.1924732744239
x73 = 2.35619449019234
x74 = -76.1836218495525
x75 = 43.1968989868597
x76 = -50.2654824574367
x77 = 80.8960108299372
x78 = 74.6128255227576
x79 = -10.2101761241668
x80 = 51.8362787842316
x81 = 26.7035375555132
x82 = 62.0464549083984
x83 = 21.2057504117311
x84 = -63.6172512351933
x85 = -22.776546738526
x86 = -81.6814089933346
x87 = -5041999.38381219
x88 = 84.037603483527
x89 = -60.4756585816035
x89 = -60.4756585816035