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cos(x)=cos(pi/5) la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
            /pi\
cos(x) = cos|--|
            \5 /
$$\cos{\left(x \right)} = \cos{\left(\frac{\pi}{5} \right)}$$
Solución detallada
Tenemos la ecuación
$$\cos{\left(x \right)} = \cos{\left(\frac{\pi}{5} \right)}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{4} + \frac{\sqrt{5}}{4} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{4} + \frac{\sqrt{5}}{4} \right)}$$
O
$$x = \pi n + \frac{\pi}{5}$$
$$x = \pi n - \frac{4 \pi}{5}$$
, donde n es cualquier número entero
Gráfica
Suma y producto de raíces [src]
suma
pi   9*pi
-- + ----
5     5  
$$\frac{\pi}{5} + \frac{9 \pi}{5}$$
=
2*pi
$$2 \pi$$
producto
pi 9*pi
--*----
5   5  
$$\frac{\pi}{5} \frac{9 \pi}{5}$$
=
    2
9*pi 
-----
  25 
$$\frac{9 \pi^{2}}{25}$$
9*pi^2/25
Respuesta rápida [src]
     pi
x1 = --
     5 
$$x_{1} = \frac{\pi}{5}$$
     9*pi
x2 = ----
      5  
$$x_{2} = \frac{9 \pi}{5}$$
x2 = 9*pi/5
Respuesta numérica [src]
x1 = -37.0707933123596
x2 = -76.026542216873
x3 = 44.6106156809751
x4 = 24.5044226980004
x5 = -88.5929128312322
x6 = -25.7610597594363
x7 = 6.91150383789754
x8 = -94.8760981384118
x9 = -82.3097275240526
x10 = -24.5044226980004
x11 = -38.3274303737955
x12 = 68.4867198482575
x13 = 93.6194610769758
x14 = 30.78760800518
x15 = -23881.7590340589
x16 = 99.9026463841554
x17 = 19.4778744522567
x18 = -68.4867198482575
x19 = 94.8760981384118
x20 = 5.65486677646163
x21 = 81.0530904626167
x22 = -19.4778744522567
x23 = -13.1946891450771
x24 = 74.7699051554371
x25 = 18.2212373908208
x26 = -69.7433569096934
x27 = -11.9380520836412
x28 = 57.1769862953342
x29 = 13.1946891450771
x30 = 82.3097275240526
x31 = 38.3274303737955
x32 = -18.2212373908208
x33 = 69.7433569096934
x34 = -44.6106156809751
x35 = 43.3539786195391
x36 = 50.8938009881547
x37 = -74.7699051554371
x38 = -0.628318530717959
x39 = -87.3362757697962
x40 = -55.9203492338983
x41 = 76.026542216873
x42 = -63.4601716025138
x43 = -49.6371639267187
x44 = -30.78760800518
x45 = 25.7610597594363
x46 = -32.0442450666159
x47 = 62.2035345410779
x48 = -6.91150383789754
x49 = 11.9380520836412
x50 = -99.9026463841554
x51 = -43.3539786195391
x52 = 37.0707933123596
x53 = 88.5929128312322
x54 = 63.4601716025138
x55 = 49.6371639267187
x56 = 0.628318530717959
x57 = -5.65486677646163
x58 = -101.159283445591
x59 = -93.6194610769758
x60 = -81.0530904626167
x61 = -220.539804282003
x62 = -50.8938009881547
x63 = 55.9203492338983
x64 = -62.2035345410779
x65 = -57.1769862953342
x66 = 87.3362757697962
x67 = 32.0442450666159
x67 = 32.0442450666159