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

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src] 
cos(2*x) + cos(x)    
----------------- = 0
        ________     
  1 + \/ sin(x)
$$\frac{\cos{\left(x \right)} + \cos{\left(2 x \right)}}{\sqrt{\sin{\left(x \right)}} + 1} = 0$$
Simplificar
Gráfica
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
  5*pi        pi   pi        5*pi
- ---- - pi - -- + -- + pi + ----
   3          3    3          3
$$\left(\left(\left(\left(- \frac{5 \pi}{3} - \pi\right) - \frac{\pi}{3}\right) + \frac{\pi}{3}\right) + \pi\right) + \frac{5 \pi}{3}$$ 
=
0
$$0$$ 
producto
-5*pi       -pi  pi    5*pi
-----*(-pi)*----*--*pi*----
  3          3   3      3
$$\frac{5 \pi}{3} \pi \frac{\pi}{3} \cdot - \frac{\pi}{3} \cdot - \frac{5 \pi}{3} \left(- \pi\right)$$ 
=
      6
-25*pi 
-------
   81
$$- \frac{25 \pi^{6}}{81}$$ 
-25*pi^6/81
Respuesta rápida [src] 
     -5*pi
x1 = -----
       3
$$x_{1} = - \frac{5 \pi}{3}$$ 
x2 = -pi
$$x_{2} = - \pi$$ 
     -pi 
x3 = ----
      3
$$x_{3} = - \frac{\pi}{3}$$ 
     pi
x4 = --
     3
$$x_{4} = \frac{\pi}{3}$$ 
x5 = pi
$$x_{5} = \pi$$ 
     5*pi
x6 = ----
      3
$$x_{6} = \frac{5 \pi}{3}$$ 
x6 = 5*pi/3
Respuesta numérica [src] 
x1 = -76.4454212373516
x2 = 89.0117918517108
x3 = -38.7463093942741
x4 = 36.6519142918809
x5 = 76.4454212373516
x6 = 32.4631240870945
x7 = 47.1238897154682 - 1.88738490602318e-7*i
x8 = -57.5958653158129
x9 = -40.8407041874092 - 1.92497361964612e-7*i
x10 = -3.14159277824728
x11 = -5.23598775598299
x12 = 24.0855436775217
x13 = 15.7079633959959 - 6.69357555717638e-8*i
x14 = -95.2949771588904
x15 = 65.973445751835 - 4.84966636689332e-9*i
x16 = 45.0294947014537
x17 = -63.8790506229925
x18 = -55.5014702134197
x19 = 53.4070752499844 - 1.05941885875543e-7*i
x20 = -65.9734457587355 - 2.72500415335158e-9*i
x21 = -34.5575190461796 - 1.0324277710217e-7*i
x22 = -7.33038285837618
x23 = 80.634211442138
x24 = -61.7846555205993
x25 = -13.6135681655558
x26 = 17.8023583703422
x27 = 47.1238899855591 - 7.73289075577684e-8*i
x28 = 3.141592899329 - 1.30079733693353e-7*i
x29 = 97.3893723972358 - 1.07146582891458e-7*i
x30 = -53.4070752218638
x31 = 99.4837673636768
x32 = -40.8407045163808 - 1.53953445008665e-7*i
x33 = -91.1061870732385
x34 = 61.7846555205993
x35 = -42.9350995990605
x36 = -30.3687289847013
x37 = -15.707963291839
x38 = 91.1061870754328 - 3.94102771255565e-8*i
x39 = 28.2743338674134
x40 = -47.1238899261052
x41 = -49.2182849062401
x42 = -24.0855436775217
x43 = 21.9911485850744 - 1.00443764234655e-9*i
x44 = -82.7286065445312
x45 = -68.0678408277789
x46 = 78.5398162389304
x47 = -21.9911485855384 - 2.79096215060324e-10*i
x48 = 34.557519085117
x49 = 1.0471975511966
x50 = -11.5191730631626
x51 = -72.2566309117546 - 6.00177058203252e-8*i
x52 = -86.9173967493176
x53 = 84.8230015192785
x54 = -17.8023583703422
x55 = 82.7286065445312
x56 = 74.3510261349584
x57 = 9.42477810216083 - 1.04645745682521e-7*i
x58 = 11.5191730631626
x59 = 59.6902605494212 - 7.02256089812397e-8*i
x60 = -70.162235930172
x61 = -19.8967534727354
x62 = 38.7463093942741
x63 = 91.1061868206746 - 2.13550003493992e-7*i
x64 = 13.6135681655558
x65 = 30.3687289847013
x66 = 40.8407043702395
x67 = 72.2566310280585
x68 = -97.3893723750251
x69 = 68.0678408277789
x70 = 70.162235930172
x71 = -9.42477806848184
x72 = -26.1799387799149
x73 = -84.823001640031 - 1.42356515538491e-7*i
x74 = -51.3126800086333
x75 = -78.5398161949917 - 1.0172235037761e-7*i
x76 = -84.8230012679754 - 2.36816828018032e-7*i
x77 = 55.5014702134197
x78 = -32.4631240870945
x79 = 57.5958653158129
x80 = 3.14159260250623 - 1.69156718916879e-7*i
x81 = -99.4837673636768
x82 = 93.2005820564972
x83 = 19.8967534727354
x84 = -93.2005820564972
x85 = -28.2743337577269 - 6.35325013122843e-8*i
x86 = 63.8790506229925
x87 = -74.3510261349584
x88 = -59.6902604501696
x89 = 26.1799387799149
x89 = 26.1799387799149
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