Sr Examen

Otras calculadoras

cos(3*x-pi/4)=1

cos(3*x-pi/4)=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|3*x - --| = 1
   \      4 /
$$\cos{\left(3 x - \frac{\pi}{4} \right)} = 1$$
Simplificar
Solución detallada
Tenemos la ecuación
$$\cos{\left(3 x - \frac{\pi}{4} \right)} = 1$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$3 x + \frac{\pi}{4} = 2 \pi n + \operatorname{asin}{\left(1 \right)}$$
$$3 x + \frac{\pi}{4} = 2 \pi n - \operatorname{asin}{\left(1 \right)} + \pi$$
O
$$3 x + \frac{\pi}{4} = 2 \pi n + \frac{\pi}{2}$$
$$3 x + \frac{\pi}{4} = 2 \pi n + \frac{\pi}{2}$$
, donde n es cualquier número entero
Transportemos
$$\frac{\pi}{4}$$
al miembro derecho de la ecuación
con el signo opuesto, en total:
$$3 x = 2 \pi n + \frac{\pi}{4}$$
$$3 x = 2 \pi n + \frac{\pi}{4}$$
Dividamos ambos miembros de la ecuación obtenida en
$$3$$
obtenemos la respuesta:
$$x_{1} = \frac{2 \pi n}{3} + \frac{\pi}{12}$$
$$x_{2} = \frac{2 \pi n}{3} + \frac{\pi}{12}$$
Gráfica
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
pi
--
12
$$\frac{\pi}{12}$$ 
=
pi
--
12
$$\frac{\pi}{12}$$ 
producto
pi
--
12
$$\frac{\pi}{12}$$ 
=
pi
--
12
$$\frac{\pi}{12}$$ 
pi/12
Respuesta rápida [src] 
     pi
x1 = --
     12
$$x_{1} = \frac{\pi}{12}$$ 
x1 = pi/12
Respuesta numérica [src] 
x1 = -64.6644488168223
x2 = -77.2308195510694
x3 = 56.8104670216825
x4 = 48.432886642189
x5 = 37.9609112688788
x6 = 77.7544183171027
x7 = 2.3561944254696
x8 = -52.0980780944246
x9 = -70.9476342579002
x10 = -62.5700535593398
x11 = 54.7160718889763
x12 = -41.6261027337242
x13 = -37.4373126002791
x14 = 46.3384915850852
x15 = -87.7027949443578
x16 = -16.4933612710947
x17 = 52.6216767905608
x18 = -10.2101759952848
x19 = 42.1497015586281
x20 = 50.5272817101232
x21 = -98.174770309605
x22 = -85.6083998925218
x23 = 10.7337747409257
x24 = 14.9225651622289
x25 = 4.45058948463671
x26 = 88.2263937070893
x27 = -20.6821517392165
x28 = 44.2440965425107
x29 = -60.4756584176213
x30 = -39.5317076725418
x31 = -8.11578093444662
x32 = 86.1319987282161
x33 = 90.3207887451617
x34 = -18.5877564243532
x35 = 31.6777260835057
x36 = -1.83259562726263
x37 = -33.2485224058352
x38 = 33.7721211611474
x39 = -50.0036830653176
x40 = -12.3045710703099
x41 = -100.269165379471
x42 = 35.8665162248298
x43 = 69.3768378311154
x44 = 6.5449845546953
x45 = 73.5656281400702
x46 = -56.286868224641
x47 = 40.0553062096054
x48 = -75.1364243772369
x49 = 27.4889358741005
x50 = -20.6821515534175
x51 = 98.6983690381338
x52 = -58.3812633115721
x53 = 81.9432084325231
x54 = -79.3252146652754
x55 = 8.63937963792691
x56 = 94.5095788659822
x57 = -96.0803752552284
x58 = 92.4151838001113
x59 = -35.3429175140413
x60 = 0.261799379286084
x61 = -83.5140048293388
x62 = -3.92699106858136
x63 = 84.0376034196564
x64 = -29.0597319144263
x65 = -20.6821517309979
x66 = 12.8281698844345
x67 = -31.1541272489312
x68 = 29.5833309902659
x69 = -81.4196097547735
x70 = -91.8915854728738
x71 = -14.3989661603031
x72 = 67.2824423751491
x73 = 75.660023236785
x74 = -93.985980238612
x75 = 60.9992577113858
x76 = 25.3945407062775
x77 = 100.792764161966
x78 = 58.9048622573859
x79 = 71.4712330177065
x80 = 79.8488133834886
x81 = -43.7204977829298
x82 = -186023.911195403
x83 = 96.6039739438038
x84 = 19.111355309138
x85 = -73.0420289677453
x86 = -45.8148928034648
x87 = 23.3001453337267
x88 = -89.7971899741286
x89 = -6.02138589675018
x90 = -54.1924731521984
x90 = -54.1924731521984
Gráfico
cos(3*x-pi/4)=1 la ecuación
    © Sr Examen