Sr Examen

Otras calculadoras

cos(x+(pi/6))=-1

cos(x+(pi/6))=-1 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

v

Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src] 
   /    pi\     
cos|x + --| = -1
   \    6 /
$$\cos{\left(x + \frac{\pi}{6} \right)} = -1$$
Simplificar
Solución detallada
Tenemos la ecuación
$$\cos{\left(x + \frac{\pi}{6} \right)} = -1$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x + \frac{\pi}{6} = \pi n + \operatorname{acos}{\left(-1 \right)}$$
$$x + \frac{\pi}{6} = \pi n - \pi + \operatorname{acos}{\left(-1 \right)}$$
O
$$x + \frac{\pi}{6} = \pi n + \pi$$
$$x + \frac{\pi}{6} = \pi n$$
, donde n es cualquier número entero
Transportemos
$$\frac{\pi}{6}$$
al miembro derecho de la ecuación
con el signo opuesto, en total:
$$x = \pi n + \frac{5 \pi}{6}$$
$$x = \pi n - \frac{\pi}{6}$$
Gráfica
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
     5*pi
x1 = ----
      6
$$x_{1} = \frac{5 \pi}{6}$$ 
x1 = 5*pi/6
Suma y producto de raíces [src] 
suma
5*pi
----
 6
$$\frac{5 \pi}{6}$$ 
=
5*pi
----
 6
$$\frac{5 \pi}{6}$$ 
producto
5*pi
----
 6
$$\frac{5 \pi}{6}$$ 
=
5*pi
----
 6
$$\frac{5 \pi}{6}$$ 
5*pi/6
Respuesta numérica [src] 
x1 = -9.94837684361999
x2 = -97.9129714856759
x3 = 90.5825886936576
x4 = -361.80675444881
x5 = 78.0162179198714
x6 = 40.3171056770577
x7 = 90.582587999292
x8 = 84.2994025838914
x9 = 59.1666609764865
x10 = 59.1666620416755
x11 = -41.3643024840352
x12 = -53.9306743428435
x13 = -16.2315625529615
x14 = 46.6002916014283
x15 = -72.7802294264824
x16 = -85.346599517262
x17 = -91.6297852224741
x18 = 34.033920359193
x19 = -28.7979322703294
x20 = 40.317105455911
x21 = -3.66519167007196
x22 = -28.7979330750006
x23 = 34.0339207847038
x24 = -16.2315621141929
x25 = -60.2138597029021
x26 = -97.9129718332953
x27 = -35.0811178580174
x28 = -9.94837719937213
x29 = -990.125283913897
x30 = -35.0811182860801
x31 = 21.4675500890045
x32 = -79.0634154430337
x33 = -53.9306741059445
x34 = 96.8657739641184
x35 = 8.90117887095619
x36 = 84.2994033661045
x37 = -47.6474880747764
x38 = -3.665191483537
x39 = 15.1843640805114
x40 = -79.0634144072739
x41 = -72.7802302304008
x42 = 78.0162175421798
x43 = 27.7507352698553
x44 = 71.7330317476983
x45 = 34.0339199446972
x46 = 71.7330324287761
x47 = -66.4970449881741
x48 = 52.8834760280739
x49 = -91.629785915216
x50 = 71.7330320678828
x51 = -22.5147473714457
x52 = 2.61799368259923
x53 = -22.5147470684883
x54 = 27.7507349796545
x55 = -60.2138590484297
x56 = -47.6474886438032
x57 = 52.8834768102045
x58 = 27.7507345972419
x59 = 2.61799455496506
x60 = 78.016217089327
x61 = 8.90117807116979
x62 = -192.160751677378
x63 = 84.2994028380602
x64 = 96.8657731852716
x65 = 90.5825886559265
x66 = -91.6297858037994
x67 = -41.3643027605
x68 = 40.317106219532
x69 = -35.0811174980382
x70 = 2.6179943910887
x71 = -60.2138592131301
x72 = 46.6002915424766
x73 = -47.6474887938562
x74 = -97.9129706275257
x75 = -85.3466006337956
x76 = -79.0634146523615
x77 = -1008.97484129336
x78 = -22.5147478349319
x79 = 128.281701088874
x80 = -85.3465999122838
x81 = 59.1666612361331
x82 = -41.3643034756348
x83 = 65.4498472464142
x84 = -3.66519092743494
x85 = 46.6002908409077
x86 = 8.90117965615139
x87 = -16.2315618892079
x88 = -66.4970442260639
x89 = 21.4675493184699
x90 = -53.9306734890854
x91 = 15.1843648857238
x92 = 65.4498464720272
x93 = -66.4970455792652
x94 = -9.94837635164697
x94 = -9.94837635164697
Gráfico
cos(x+(pi/6))=-1 la ecuación
    © Sr Examen