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sin(2*x)=sqrt(2)*sin(x+pi/2) la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
             ___    /    pi\
sin(2*x) = \/ 2 *sin|x + --|
                    \    2 /
$$\sin{\left(2 x \right)} = \sqrt{2} \sin{\left(x + \frac{\pi}{2} \right)}$$
Gráfica
Respuesta rápida [src]
     -pi 
x1 = ----
      2  
$$x_{1} = - \frac{\pi}{2}$$
     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
Suma y producto de raíces [src]
suma
  pi   pi   pi   3*pi
- -- + -- + -- + ----
  2    4    2     4  
$$\left(\left(- \frac{\pi}{2} + \frac{\pi}{4}\right) + \frac{\pi}{2}\right) + \frac{3 \pi}{4}$$
=
pi
$$\pi$$
producto
-pi  pi pi 3*pi
----*--*--*----
 2   4  2   4  
$$\frac{3 \pi}{4} \frac{\pi}{2} \cdot - \frac{\pi}{2} \frac{\pi}{4}$$
=
     4
-3*pi 
------
  64  
$$- \frac{3 \pi^{4}}{64}$$
-3*pi^4/64
Respuesta numérica [src]
x1 = -64.4026493985908
x2 = 2.35619449019234
x3 = -23.5619449019235
x4 = -29.845130209103
x5 = 57.3340659280137
x6 = -11.7809724509617
x7 = 46.3384916404494
x8 = 42.4115008234622
x9 = 40.0553063332699
x10 = 4.71238898038469
x11 = 58.9048622548086
x12 = 36.1283155162826
x13 = 33.7721210260903
x14 = 23.5619449019235
x15 = 71.4712328691678
x16 = 51.0508806208341
x17 = -80.1106126665397
x18 = 86.3937979737193
x19 = -29.0597320457056
x20 = -18.0641577581413
x21 = 64.4026493985908
x22 = -80.8960108299372
x23 = -83.2522053201295
x24 = -22.776546738526
x25 = -95.8185759344887
x26 = -85.6083998103219
x27 = 21.2057504117311
x28 = -1.5707963267949
x29 = 76.1836218495525
x30 = 44.7676953136546
x31 = -62.0464549083984
x32 = 13.3517687777566
x33 = 73.8274273593601
x34 = 7.06858347057703
x35 = -39.2699081698724
x36 = 32.2013246992954
x37 = 67.5442420521806
x38 = 88.7499924639117
x39 = -66.7588438887831
x40 = -16.4933614313464
x41 = -10.2101761241668
x42 = -47.9092879672443
x43 = -73.0420291959627
x44 = -5.49778714378214
x45 = -51.8362787842316
x46 = 58.1194640914112
x47 = -60.4756585816035
x48 = -93.4623814442964
x49 = -73.8274273593601
x50 = 51.8362787842316
x51 = -87.1791961371168
x52 = 82.4668071567321
x53 = 29.845130209103
x54 = -45.553093477052
x55 = -54.1924732744239
x56 = 80.1106126665397
x57 = -58.1194640914112
x58 = -98.174770424681
x59 = 38.484510006475
x60 = -36.1283155162826
x61 = -43.1968989868597
x62 = -49.4800842940392
x63 = 27.4889357189107
x64 = -41.6261026600648
x65 = -67.5442420521806
x66 = -91.8915851175014
x67 = 77.7544181763474
x68 = 14.9225651045515
x69 = 25.9181393921158
x70 = -7.85398163397448
x71 = 48.6946861306418
x72 = -55.7632696012188
x73 = 95.0331777710912
x74 = -36.9137136796801
x75 = 7.85398163397448
x76 = -14.1371669411541
x77 = -3.92699081698724
x78 = 90.3207887907066
x79 = -30.6305283725005
x80 = 14.1371669411541
x81 = 65.1880475619882
x82 = 69.9004365423729
x83 = 20.4203522483337
x84 = 95.8185759344887
x85 = -89.5353906273091
x86 = 84.037603483527
x87 = 92.6769832808989
x88 = 102.887159405066
x89 = -99.7455667514759
x90 = 0.785398163397448
x91 = 101.316363078271
x92 = -20.4203522483337
x92 = -20.4203522483337