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

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
  ___    2         /    pi\
\/ 2 *cos (x) = sin|x + --|
                   \    2 /
$$\sqrt{2} \cos^{2}{\left(x \right)} = \sin{\left(x + \frac{\pi}{2} \right)}$$
Gráfica
Suma y producto de raíces [src]
suma
pi   pi   3*pi   7*pi
-- + -- + ---- + ----
4    2     2      4  
$$\frac{7 \pi}{4} + \left(\left(\frac{\pi}{4} + \frac{\pi}{2}\right) + \frac{3 \pi}{2}\right)$$
=
4*pi
$$4 \pi$$
producto
pi pi 3*pi 7*pi
--*--*----*----
4  2   2    4  
$$\frac{7 \pi}{4} \frac{3 \pi}{2} \frac{\pi}{4} \frac{\pi}{2}$$
=
     4
21*pi 
------
  64  
$$\frac{21 \pi^{4}}{64}$$
21*pi^4/64
Respuesta rápida [src]
     pi
x1 = --
     4 
$$x_{1} = \frac{\pi}{4}$$
     pi
x2 = --
     2 
$$x_{2} = \frac{\pi}{2}$$
     3*pi
x3 = ----
      2  
$$x_{3} = \frac{3 \pi}{2}$$
     7*pi
x4 = ----
      4  
$$x_{4} = \frac{7 \pi}{4}$$
x4 = 7*pi/4
Respuesta numérica [src]
x1 = 4.71238898038469
x2 = 17.2787595947439
x3 = -55.7632696012188
x4 = 7.85398163397448
x5 = 120.16591899981
x6 = 99.7455667514759
x7 = -39.2699081698724
x8 = 38.484510006475
x9 = -32.2013246992954
x10 = 95.8185759344887
x11 = -86.3937979737193
x12 = -10.9955742875643
x13 = -48.6946861306418
x14 = -45.553093477052
x15 = 26.7035375555132
x16 = 10.9955742875643
x17 = 62.0464549083984
x18 = 25.9181393921158
x19 = 32.9867228626928
x20 = -19.6349540849362
x21 = -82.4668071567321
x22 = 24.3473430653209
x23 = 76.1836218495525
x24 = -98.9601685880785
x25 = 48.6946861306418
x26 = -58.1194640914112
x27 = 39.2699081698724
x28 = -49.4800842940392
x29 = 82.4668071567321
x30 = -755.553033188345
x31 = -80.1106126665397
x32 = -83.2522053201295
x33 = 98.9601685880785
x34 = -93.4623814442964
x35 = 86.3937979737193
x36 = -99.7455667514759
x37 = 45.553093477052
x38 = 51.8362787842316
x39 = 76.9690200129499
x40 = -26.7035375555132
x41 = -5.49778714378214
x42 = -88.7499924639117
x43 = 83.2522053201295
x44 = -14.1371669411541
x45 = -11.7809724509617
x46 = 20.4203522483337
x47 = -54.9778714378214
x48 = -73.8274273593601
x49 = -44.7676953136546
x50 = -18.0641577581413
x51 = -76.9690200129499
x52 = -29.845130209103
x53 = -89.5353906273091
x54 = 64.4026493985908
x55 = -62.0464549083984
x56 = -92.6769832808989
x57 = 61.261056745001
x58 = 18.0641577581413
x59 = 29.845130209103
x60 = 11.7809724509617
x61 = -51.8362787842316
x62 = 69.9004365423729
x63 = 88.7499924639117
x64 = 92.6769832808989
x65 = 55.7632696012188
x66 = -63.6172512351933
x67 = -67.5442420521806
x68 = -36.1283155162826
x69 = -7.85398163397448
x70 = 54.9778714378214
x71 = 14.1371669411541
x72 = 89.5353906273091
x73 = 80.1106126665397
x74 = -25.9181393921158
x75 = 42.4115008234622
x76 = -69.9004365423729
x77 = 36.1283155162826
x78 = -1.5707963267949
x79 = -95.8185759344887
x80 = -23.5619449019235
x81 = 32.2013246992954
x82 = -32.9867228626928
x83 = 67.5442420521806
x84 = -4.71238898038469
x85 = -76.1836218495525
x86 = -70.6858347057703
x87 = 73.8274273593601
x88 = 58.1194640914112
x89 = 1.5707963267949
x90 = 68.329640215578
x91 = -42.4115008234622
x91 = -42.4115008234622