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cos(x-30)=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
cos(x - 30) = 0
cos⁡(x−30)=0\cos{\left(x - 30 \right)} = 0
Simplificar
Solución detallada
Tenemos la ecuación
cos⁡(x−30)=0\cos{\left(x - 30 \right)} = 0
es la ecuación trigonométrica más simple
cambiando el signo de 0

Obtenemos:
cos⁡(x−30)=0\cos{\left(x - 30 \right)} = 0
Esta ecuación se reorganiza en
x−30=πn+acos⁡(0)x - 30 = \pi n + \operatorname{acos}{\left(0 \right)}
x−30=πn−π+acos⁡(0)x - 30 = \pi n - \pi + \operatorname{acos}{\left(0 \right)}
O
x−30=πn+π2x - 30 = \pi n + \frac{\pi}{2}
x−30=πn−π2x - 30 = \pi n - \frac{\pi}{2}
, donde n es cualquier número entero
Transportemos
−30-30
al miembro derecho de la ecuación
con el signo opuesto, en total:
x=πn+π2+30x = \pi n + \frac{\pi}{2} + 30
x=πn−π2+30x = \pi n - \frac{\pi}{2} + 30
Gráfica
0-80-60-40-2020406080-1001002-2
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
          pi
x1 = 30 + --
          2
x1=π2+30x_{1} = \frac{\pi}{2} + 30 
          3*pi
x2 = 30 + ----
           2
x2=3π2+30x_{2} = \frac{3 \pi}{2} + 30 
x2 = 3*pi/2 + 30
Suma y producto de raíces [src] 
suma
     pi        3*pi
30 + -- + 30 + ----
     2          2
(π2+30)+(3π2+30)\left(\frac{\pi}{2} + 30\right) + \left(\frac{3 \pi}{2} + 30\right) 
=
60 + 2*pi
2π+602 \pi + 60 
producto
/     pi\ /     3*pi\
|30 + --|*|30 + ----|
\     2 / \      2  /
(π2+30)(3π2+30)\left(\frac{\pi}{2} + 30\right) \left(\frac{3 \pi}{2} + 30\right) 
=
3*(20 + pi)*(60 + pi)
---------------------
          4
3(π+20)(π+60)4\frac{3 \left(\pi + 20\right) \left(\pi + 60\right)}{4} 
3*(20 + pi)*(60 + pi)/4
Respuesta numérica [src] 
x1 = -2.98672286269283
x2 = 84.9778714378214
x3 = 69.2699081698724
x4 = -87.8097245096172
x5 = 100.68583470577
x6 = -34.4026493985908
x7 = 50.4203522483337
x8 = -241.747764535517
x9 = -21.8362787842316
x10 = 53.5619449019234
x11 = -84.6681318560275
x12 = -12.4115008234622
x13 = 22.1460183660255
x14 = 19.0044257124357
x15 = 56.7035375555132
x16 = 81.8362787842316
x17 = -46.9690200129499
x18 = -15.553093477052
x19 = -65.8185759344887
x20 = -50.1106126665397
x21 = 62.9867228626928
x22 = -78.3849465488479
x23 = 28.4292036732051
x24 = -37.5442420521806
x25 = -59.5353906273091
x26 = 94.4026493985908
x27 = -314.004395568082
x28 = 47.2787595947439
x29 = 0.154869790896964
x30 = 59.845130209103
x31 = 91.261056745001
x32 = -56.3937979737193
x33 = -24.9778714378214
x34 = 3.29646244448676
x35 = -2236.65909956504
x36 = 12.7212404052561
x37 = 25.2876110196153
x38 = 31.5707963267949
x39 = -53.2522053201295
x40 = 75.553093477052
x41 = -72.1017612416683
x42 = -28.1194640914112
x43 = 78.6946861306418
x44 = -100.376095123976
x45 = -97.2345024703866
x46 = -6.12831551628262
x47 = 34.7123889803847
x48 = -357.986692718339
x49 = 66.1283155162826
x50 = -43.8274273593601
x51 = -18.6946861306418
x52 = -68.9601685880785
x53 = -3468.16341977223
x54 = 40.9955742875643
x55 = 6.43805509807655
x56 = 97.5442420521806
x57 = 9.57964775166634
x58 = -94.0929098167968
x59 = -75.2433538952581
x60 = -9.26990816987242
x61 = 72.4115008234622
x62 = -90.951317163207
x63 = 37.8539816339745
x64 = 15.8628330588459
x65 = -81.5265392024377
x66 = -31.261056745001
x67 = -40.6858347057703
x68 = -62.6769832808989
x69 = 44.1371669411541
x70 = 88.1194640914112
x70 = 88.1194640914112
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