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- La ecuación:
-
Ecuación x+2/x=3
-
Ecuación 8*x-3*(2*x+1)=2*x+4
- Ecuación x+y+2=0
-
Ecuación 1+sin(x)=0
- Expresar {x} en función de y en la ecuación:
- 18*x+20*y=-2
- 18*x-8*y=-2
- 1*x+5*y=-11
- -3*x-20*y=-13
- Integral de d{x}:
- cos2x
- Derivada de:
-
cos2x
-
1/2
- Gráfico de la función y =:
-
cos2x
- Suma de la serie:
-
1/2
- Límite de la función:
-
1/2
-
Expresiones idénticas
- cos dos x= uno /2
- coseno de 2x es igual a 1 dividir por 2
- coseno de dos x es igual a uno dividir por 2
- cos2x=1 dividir por 2
-
Expresiones semejantes
- cos(2*x)+sqrt(2)*sin(x)+1=0
- cos(2*x)+3*sin(x)-2=0
- cos(2x)=1/2
cos2x=1/2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Tenemos la ecuación
$$\cos{\left(2 x \right)} = \frac{1}{2}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$2 x = \pi n + \operatorname{acos}{\left(\frac{1}{2} \right)}$$
$$2 x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{2} \right)}$$
O
$$2 x = \pi n + \frac{\pi}{3}$$
$$2 x = \pi n - \frac{2 \pi}{3}$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$2$$
obtenemos la respuesta:
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{6}$$
$$x_{2} = \frac{\pi n}{2} - \frac{\pi}{3}$$
$$\cos{\left(2 x \right)} = \frac{1}{2}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$2 x = \pi n + \operatorname{acos}{\left(\frac{1}{2} \right)}$$
$$2 x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{2} \right)}$$
O
$$2 x = \pi n + \frac{\pi}{3}$$
$$2 x = \pi n - \frac{2 \pi}{3}$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$2$$
obtenemos la respuesta:
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{6}$$
$$x_{2} = \frac{\pi n}{2} - \frac{\pi}{3}$$
Respuesta rápida
[src]
pi
x1 = --
6
$$x_{1} = \frac{\pi}{6}$$
5*pi
x2 = ----
6
$$x_{2} = \frac{5 \pi}{6}$$
x2 = 5*pi/6
Suma y producto de raíces
[src]
suma
pi 5*pi -- + ---- 6 6
$$\frac{\pi}{6} + \frac{5 \pi}{6}$$
=
pi
$$\pi$$
producto
pi 5*pi --*---- 6 6
$$\frac{\pi}{6} \frac{5 \pi}{6}$$
=
2 5*pi ----- 36
$$\frac{5 \pi^{2}}{36}$$
5*pi^2/36
Respuesta numérica
[src]
x1 = -3.66519142918809
x2 = 38.2227106186758
x3 = 88.4881930761125
x4 = 5.75958653158129
x5 = -82.2050077689329
x6 = 131.423292675173
x7 = 97.9129710368819
x8 = -68.5914396033772
x9 = 68.5914396033772
x10 = 30.8923277602996
x11 = 96.8657734856853
x12 = -9.94837673636768
x13 = -46.6002910282486
x14 = -56.025068989018
x15 = -24.60914245312
x16 = -16.2315620435473
x17 = 60.2138591938044
x18 = 25.6563400043166
x19 = -84.2994028713261
x20 = -97.9129710368819
x21 = -53.9306738866248
x22 = -19.3731546971371
x23 = 62.3082542961976
x24 = -100.007366139275
x25 = 49.7418836818384
x26 = -2685.53812004368
x27 = 24.60914245312
x28 = -75.9218224617533
x29 = 90.5825881785057
x30 = 66.497044500984
x31 = 93.7241808320955
x32 = -81.1578102177363
x33 = -78.0162175641465
x34 = -35.081117965086
x35 = -91.6297857297023
x36 = 100.007366139275
x37 = 34.0339204138894
x38 = -63.3554518473942
x39 = 69.6386371545737
x40 = 91.6297857297023
x41 = 53.9306738866248
x42 = 2.61799387799149
x43 = -85.3466004225227
x44 = -69.6386371545737
x45 = 125.140107367993
x46 = 12.0427718387609
x47 = 74.8746249105567
x48 = -12.0427718387609
x49 = 82.2050077689329
x50 = -21.4675497995303
x51 = -47.6474885794452
x52 = -13.0899693899575
x53 = 41.3643032722656
x54 = 9.94837673636768
x55 = 75.9218224617533
x56 = -49.7418836818384
x57 = 56.025068989018
x58 = 44.5058959258554
x59 = 27.7507351067098
x60 = -93.7241808320955
x61 = -1152.44090509186
x62 = -43.4586983746588
x63 = 52.8834763354282
x64 = 63.3554518473942
x65 = 19.3731546971371
x66 = -71.733032256967
x67 = 3.66519142918809
x68 = -87.4409955249159
x69 = -40.317105721069
x70 = 46.6002910282486
x71 = 78.0162175641465
x72 = 0.523598775598299
x73 = 18.3259571459405
x74 = -25.6563400043166
x75 = 31.9395253114962
x76 = 47.6474885794452
x77 = -5.75958653158129
x78 = -7272.26339428477
x79 = -90.5825881785057
x80 = -27.7507351067098
x81 = -34.0339204138894
x82 = -65.4498469497874
x83 = 8.90117918517108
x84 = -62.3082542961976
x85 = -18.3259571459405
x86 = -41.3643032722656
x87 = -31.9395253114962
x88 = 22.5147473507269
x89 = 84.2994028713261
x90 = 16.2315620435473
x91 = -60.2138591938044
x92 = -38.2227106186758
x93 = 40.317105721069
x94 = 85.3466004225227
x95 = -217.293491873294
x96 = 71.733032256967
x97 = -2.61799387799149
x97 = -2.61799387799149
Gráfico