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cos(x)=sqrt((1+sin(x))/2)

cos(x)=sqrt((1+sin(x))/2) la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
             ____________
            / 1 + sin(x) 
cos(x) =   /  ---------- 
         \/       2      
$$\cos{\left(x \right)} = \sqrt{\frac{\sin{\left(x \right)} + 1}{2}}$$
Gráfica
Respuesta rápida [src]
     -pi 
x1 = ----
      2  
$$x_{1} = - \frac{\pi}{2}$$
     pi
x2 = --
     6 
$$x_{2} = \frac{\pi}{6}$$
x2 = pi/6
Suma y producto de raíces [src]
suma
  pi   pi
- -- + --
  2    6 
$$- \frac{\pi}{2} + \frac{\pi}{6}$$
=
-pi 
----
 3  
$$- \frac{\pi}{3}$$
producto
-pi  pi
----*--
 2   6 
$$- \frac{\pi}{2} \frac{\pi}{6}$$
=
   2 
-pi  
-----
  12 
$$- \frac{\pi^{2}}{12}$$
-pi^2/12
Respuesta numérica [src]
x1 = 4.71238898038469
x2 = -20.4203522483337
x3 = -14.1371669411541
x4 = -32.9867228626928
x5 = 10.9955742875643
x6 = -49.7418836818384
x7 = -81.1578102177363
x8 = 38.2227106186758
x9 = 42.4115008234622
x10 = -74.8746249105567
x11 = 88.4881930761125
x12 = 31.9395253114962
x13 = -187.971960439789
x14 = -95.8185759344887
x15 = 44.5058959258554
x16 = -7.85398163397448
x17 = -5.75958653158129
x18 = 13.0899693899575
x19 = -93.7241808320955
x20 = 80.1106126665397
x21 = -68.5914396033772
x22 = -56.025068989018
x23 = -30.8923277602996
x24 = -24.60914245312
x25 = 94.7713783832921
x26 = 17.2787595947439
x27 = 61.261056745001
x28 = 29.845130209103
x29 = 23.5619449019235
x30 = -70.6858347057703
x31 = 69.6386371545737
x32 = -43.4586983746588
x33 = 63.3554518473942
x34 = 19.3731546971371
x35 = -26.7035375555132
x36 = -18.3259571459405
x37 = -62.3082542961976
x38 = -106.290551446455
x39 = 25.6563400043166
x40 = 6.80678408277789
x41 = 92.6769832808989
x42 = 50.789081233035
x43 = -87.4409955249159
x44 = 86.3937979737193
x45 = -58.1194640914112
x46 = 36.1283155162826
x47 = -45.553093477052
x48 = -51.8362787842316
x49 = 67.5442420521806
x50 = -100.007366139275
x51 = 54.9778714378214
x52 = -39.2699081698724
x53 = -12.0427718387609
x54 = -83.2522053201295
x55 = -76.9690200129499
x56 = 48.6946861306418
x57 = -64.4026493985908
x58 = 82.2050077689329
x59 = 57.0722665402146
x60 = 73.8274273593601
x61 = -1.5707963267949
x62 = -37.1755130674792
x63 = 98.9601685880785
x64 = 0.523598775598299
x65 = -89.5353906273091
x66 = 75.9218224617533
x66 = 75.9218224617533
Gráfico
cos(x)=sqrt((1+sin(x))/2) la ecuación