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ln(2-cos(x)) la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
log(2 - cos(x)) = 0
log⁡(2−cos⁡(x))=0\log{\left(2 - \cos{\left(x \right)} \right)} = 0
Simplificar
Solución detallada
Tenemos la ecuación
log⁡(2−cos⁡(x))=0\log{\left(2 - \cos{\left(x \right)} \right)} = 0
cambiamos
log⁡(2−cos⁡(x))=0\log{\left(2 - \cos{\left(x \right)} \right)} = 0
log⁡(2−cos⁡(x))=0\log{\left(2 - \cos{\left(x \right)} \right)} = 0
Sustituimos
w=cos⁡(x)w = \cos{\left(x \right)}
Tenemos la ecuación
log⁡(2−w)=0\log{\left(2 - w \right)} = 0
log⁡(2−w)=0\log{\left(2 - w \right)} = 0
Es la ecuación de la forma:
log(v)=p

Por definición log
v=e^p

entonces
2−w=e012 - w = e^{\frac{0}{1}}
simplificamos
2−w=12 - w = 1
−w=−1- w = -1
w=1w = 1
hacemos cambio inverso
cos⁡(x)=w\cos{\left(x \right)} = w
Tenemos la ecuación
cos⁡(x)=w\cos{\left(x \right)} = w
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
x=πn+acos⁡(w)x = \pi n + \operatorname{acos}{\left(w \right)}
x=πn+acos⁡(w)−πx = \pi n + \operatorname{acos}{\left(w \right)} - \pi
O
x=πn+acos⁡(w)x = \pi n + \operatorname{acos}{\left(w \right)}
x=πn+acos⁡(w)−πx = \pi n + \operatorname{acos}{\left(w \right)} - \pi
, donde n es cualquier número entero
sustituimos w:
Gráfica
0-80-60-40-2020406080-10010002
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
x1 = 0
x1=0x_{1} = 0 
x2 = 2*pi
x2=2πx_{2} = 2 \pi 
x2 = 2*pi
Suma y producto de raíces [src] 
suma
2*pi
2π2 \pi 
=
2*pi
2π2 \pi 
producto
0*2*pi
0⋅2π0 \cdot 2 \pi 
=
0
00 
0
Respuesta numérica [src] 
x1 = 471.238897997772
x2 = 1.65907061351532e-7
x3 = 0.0
x4 = 25.1327409295962
x5 = 12.5663704509757
x6 = 43.9822971694279
x7 = 56.5486679549878
x8 = 87.9645943357613
x9 = -31.41592659804
x10 = -12.5663709007493
x11 = -75.3982234665557
x12 = 94.2477796093525
x13 = 12.5663702384678
x14 = -31.4159267062921
x15 = -56.5486675079998
x16 = 87.9645935301424
x17 = 43.9822972815896
x18 = -62.8318533729422
x19 = -50.2654826259573
x20 = -18.8495562217774
x21 = -106.814150962879
x22 = -25.1327414875349
x23 = -81.681409036985
x24 = 62.8318533627858
x25 = -6.28318548766167
x26 = -69.1150386418008
x27 = 75.3982233942965
x28 = -87.9645943587701
x29 = 31.415926800871
x30 = 43.9822963773283
x31 = -100.53096466271
x32 = -43.9822969475826
x33 = 62.8318521656398
x34 = -94.2477797633436
x35 = -69.1150380803451
x36 = -37.6991119153289
x37 = -56.548668047785
x38 = -87.9645949997818
x39 = 6.28318528425031
x40 = -94.2477794523601
x41 = 37.6991116514814
x42 = 18981.5028117004
x43 = -43.9822971745782
x44 = 18.849555666914
x45 = -12.5663703534729
x46 = -75.3982238633872
x47 = 50.2654832291066
x48 = 81.6814087914149
x49 = -37.6991118771541
x50 = -37.6991110986159
x51 = -43.9822978837464
x52 = 56.5486676084168
x53 = 87.9645943994199
x54 = 6.28318520432519
x55 = 50.2654824463472
x56 = -31.4159263253384
x57 = -25.1327409323502
x58 = 12.5663708151926
x59 = -6.28318513695273
x60 = 6.2831854736161
x61 = 62.8318528215448
x62 = -87.9645940588686
x63 = 50.2654823218943
x64 = -81.681409038012
x65 = 94.2477794373133
x66 = 37.6991120204243
x67 = 100.530964766032
x68 = 6.28318513123834
x69 = 75.3982239550318
x70 = -18.8495556173862
x71 = 31.4159262466159
x72 = 69.1150380811757
x73 = -62.8318527689446
x74 = 25.1327415339784
x75 = -81.6814083101974
x76 = 18.849556215364
x77 = -12032.2998626893
x78 = 81.6814091775934
x79 = -50.2654822945446
x80 = 69.1150386851472
x81 = -7.59131855319776e-7
x82 = 94.2477803647286
x83 = 6.28318607700903
x83 = 6.28318607700903
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