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cos(30°-2x)=1/2 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
   /30*pi      \      
cos|----- - 2*x| = 1/2
   \ 360       /
cos⁡(−2x+30π360)=12\cos{\left(- 2 x + \frac{30 \pi}{360} \right)} = \frac{1}{2}
Simplificar
Solución detallada
Tenemos la ecuación
cos⁡(−2x+30π360)=12\cos{\left(- 2 x + \frac{30 \pi}{360} \right)} = \frac{1}{2}
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
2x+5π12=2πn+asin⁡(12)2 x + \frac{5 \pi}{12} = 2 \pi n + \operatorname{asin}{\left(\frac{1}{2} \right)}
2x+5π12=2πn−asin⁡(12)+π2 x + \frac{5 \pi}{12} = 2 \pi n - \operatorname{asin}{\left(\frac{1}{2} \right)} + \pi
O
2x+5π12=2πn+π62 x + \frac{5 \pi}{12} = 2 \pi n + \frac{\pi}{6}
2x+5π12=2πn+5π62 x + \frac{5 \pi}{12} = 2 \pi n + \frac{5 \pi}{6}
, donde n es cualquier número entero
Transportemos
5π12\frac{5 \pi}{12}
al miembro derecho de la ecuación
con el signo opuesto, en total:
2x=2πn−π42 x = 2 \pi n - \frac{\pi}{4}
2x=2πn+5π122 x = 2 \pi n + \frac{5 \pi}{12}
Dividamos ambos miembros de la ecuación obtenida en
22
obtenemos la respuesta:
x1=πn−π8x_{1} = \pi n - \frac{\pi}{8}
x2=πn+5π24x_{2} = \pi n + \frac{5 \pi}{24}
Gráfica
0-80-60-40-2020406080-1001002-2
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
  pi   5*pi
- -- + ----
  8     24
−π8+5π24- \frac{\pi}{8} + \frac{5 \pi}{24} 
=
pi
--
12
π12\frac{\pi}{12} 
producto
-pi  5*pi
----*----
 8    24
−π85π24- \frac{\pi}{8} \frac{5 \pi}{24} 
=
     2
-5*pi 
------
 192
−5π2192- \frac{5 \pi^{2}}{192} 
-5*pi^2/192
Respuesta rápida [src] 
     -pi 
x1 = ----
      8
x1=−π8x_{1} = - \frac{\pi}{8} 
     5*pi
x2 = ----
      24
x2=5π24x_{2} = \frac{5 \pi}{24} 
x2 = 5*pi/24
Respuesta numérica [src] 
x1 = -55.8941692951184
x2 = 90.7134878724053
x3 = -103.018059098965
x4 = -62.177354602298
x5 = 27.8816348006094
x6 = 1231.1116211255
x7 = 25.7872396982162
x8 = -77.885317870247
x9 = -27.6198354128103
x10 = 76.0527221556529
x11 = -19.2422550032375
x12 = 19.5040543910366
x13 = -47.5165888855456
x14 = 115.846229101124
x15 = -9.8174770424681
x16 = 82.3359074628325
x17 = 16.3624617374468
x18 = 63.4863515412937
x19 = 56.1559686829176
x20 = -3.53429173528852
x21 = 93.8550805259951
x22 = 3.79609112308767
x23 = 91.7606854236019
x24 = -56.941366846315
x25 = -5.62868683768171
x26 = 46.7311907221482
x27 = 12.1736715326604
x28 = -69.5077374606742
x29 = -91.4988860358027
x30 = 71.8639319508665
x31 = -90.4516884846061
x32 = -84.1685031774265
x33 = 49.872783375738
x34 = -6.67588438887831
x35 = -82.0741080750334
x36 = -33.9030207199899
x37 = -16.1006623496477
x38 = 62.4391539900971
x39 = -60.0829594999048
x40 = 2.74889357189107
x41 = 84.4303025652257
x42 = -11.9118721448613
x43 = 106.421451140354
x44 = -97.7820713429823
x45 = -68.4605399094776
x46 = -93.5932811381959
x47 = -40.1862060271694
x48 = 47.7783882733448
x49 = 10.0792764302673
x50 = 54.0615735805244
x51 = -75.7909227678538
x52 = 40.4480054149686
x53 = -31.8086256175967
x54 = -53.7997741927252
x55 = -38.0918109247762
x56 = 85.4775001164223
x57 = 69.7695368484733
x58 = -25.5254403104171
x59 = -2.48709418409192
x60 = -99.8764664453755
x61 = 34.164820107789
x62 = 18.45685683984
x63 = -85.2157007286231
x64 = 38.3536103125754
x65 = -63.2245521534946
x66 = 5.89048622548086
x67 = -46.469391334349
x68 = -24.4782427592205
x69 = 286.539429946169
x70 = -71.6021325630674
x71 = 32.0704250053958
x72 = -18.1950574520409
x73 = 60.3447588877039
x74 = 68.7223392972767
x75 = 13.220869083857
x76 = 41.4952029661652
x77 = -41.233403578366
x78 = -49.6109839879388
x79 = 24.7400421470196
x80 = 100.138265833175
x81 = 98.0438707307815
x82 = 78.1471172580461
x82 = 78.1471172580461
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