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- La ecuación:
-
Ecuación (x-3)*(x+2)=0
-
Ecuación (11x+14)-(5x-8)=25
-
Ecuación z^2-6*z+10=0
-
Ecuación 4/(x-4)=-5
- Expresar {x} en función de y en la ecuación:
- -7*x-13*y=5
- 15*x+1*y=19
- 7*x-1*y=-7
- -11*x-14*y=-3
- Derivada de:
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2cos3x
- Gráfico de la función y =:
- 2cos3x
-
Expresiones idénticas
- 2cos tres x=√(3)
- 2 coseno de 3x es igual a √(3)
- 2 coseno de tres x es igual a √(3)
- 2cos3x=√3
-
Expresiones semejantes
- y^n+y=2*cos(3x)-3*sin(3x)
- tg*π(2x−21)/6=√3/3
- sin(2x)+sin(pi-8x)=sqrt(2)*cos(3x)
- √3ctg(x+pi)-3=0
- tan(x/2)=-√3/3
- cos(x)=√3
- 2cos(3x)=sqrt3
2cos3x=√(3) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Tenemos la ecuación
$$2 \cos{\left(3 x \right)} = \sqrt{3}$$
es la ecuación trigonométrica más simple
La ecuación se convierte en
$$\cos{\left(3 x \right)} = \frac{\sqrt{3}}{2}$$
Esta ecuación se reorganiza en
$$3 x = \pi n + \operatorname{acos}{\left(\frac{\sqrt{3}}{2} \right)}$$
$$3 x = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{3}}{2} \right)}$$
O
$$3 x = \pi n + \frac{\pi}{6}$$
$$3 x = \pi n - \frac{5 \pi}{6}$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$3$$
obtenemos la respuesta:
$$x_{1} = \frac{\pi n}{3} + \frac{\pi}{18}$$
$$x_{2} = \frac{\pi n}{3} - \frac{5 \pi}{18}$$
$$2 \cos{\left(3 x \right)} = \sqrt{3}$$
es la ecuación trigonométrica más simple
Dividamos ambos miembros de la ecuación en 2
La ecuación se convierte en
$$\cos{\left(3 x \right)} = \frac{\sqrt{3}}{2}$$
Esta ecuación se reorganiza en
$$3 x = \pi n + \operatorname{acos}{\left(\frac{\sqrt{3}}{2} \right)}$$
$$3 x = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{3}}{2} \right)}$$
O
$$3 x = \pi n + \frac{\pi}{6}$$
$$3 x = \pi n - \frac{5 \pi}{6}$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$3$$
obtenemos la respuesta:
$$x_{1} = \frac{\pi n}{3} + \frac{\pi}{18}$$
$$x_{2} = \frac{\pi n}{3} - \frac{5 \pi}{18}$$
Respuesta rápida
[src]
pi
x1 = --
18
$$x_{1} = \frac{\pi}{18}$$
11*pi
x2 = -----
18
$$x_{2} = \frac{11 \pi}{18}$$
x2 = 11*pi/18
Suma y producto de raíces
[src]
suma
pi 11*pi -- + ----- 18 18
$$\frac{\pi}{18} + \frac{11 \pi}{18}$$
=
2*pi ---- 3
$$\frac{2 \pi}{3}$$
producto
pi 11*pi --*----- 18 18
$$\frac{\pi}{18} \frac{11 \pi}{18}$$
=
2 11*pi ------ 324
$$\frac{11 \pi^{2}}{324}$$
11*pi^2/324
Respuesta numérica
[src]
x1 = -35.7792496658838
x2 = -60.9119908946021
x3 = -87.7900613753148
x4 = -52.1853446346305
x5 = 94.0732466824944
x6 = 83.9503370209273
x7 = 25.3072741539178
x8 = 2.26892802759263
x9 = -50.0909495322373
x10 = -75.5727566113545
x11 = -86.0447321233204
x12 = -81.5068760681352
x13 = 96.1676417848876
x14 = -73.4783615089613
x15 = 56.3741348394168
x16 = -25.3072741539178
x17 = 16.5806278939461
x18 = 50.0909495322373
x19 = -14.4862327915529
x20 = -6.10865238198015
x21 = -16.929693744345
x22 = 4.01425727958696
x23 = -1.91986217719376
x24 = -20.7694180987325
x25 = -79.412480965742
x26 = 31.5904594610974
x27 = -71.3839664065681
x28 = -4.01425727958696
x29 = 67.1951762017817
x30 = 6.10865238198015
x31 = 100.356431989674
x32 = -22.8638132011257
x33 = 37.873644768277
x34 = 77.6671517137477
x35 = 33.6848545634906
x36 = -47.9965544298441
x37 = -77.6671517137477
x38 = -45.9021593274509
x39 = -91.9788515801012
x40 = 44.1568300754565
x41 = -66.8461103513828
x42 = -79.7615468161409
x43 = 42.0624349730633
x44 = 54.2797397370236
x45 = 90.2335223281068
x46 = 98.2620368872808
x47 = -33.6848545634906
x48 = 18.6750229963393
x49 = 0.174532925199433
x50 = -41.7133691226645
x51 = 14.4862327915529
x52 = 29.1469985083053
x53 = -29.4960643587042
x54 = 35.7792496658838
x55 = -27.401669256311
x56 = 10.2974425867665
x57 = 79.7615468161409
x58 = -10.6465084371654
x59 = -10.2974425867665
x60 = -81.8559419185341
x61 = 12.3918376891597
x62 = 100.705497840073
x63 = 60.5629250442032
x64 = 27.0526034059121
x65 = 81.8559419185341
x66 = -94.0732466824944
x67 = -96.1676417848876
x68 = -12.3918376891597
x69 = 52.1853446346305
x70 = 75.5727566113545
x71 = -31.5904594610974
x72 = -37.873644768277
x73 = -43.8077642250577
x74 = -83.9503370209273
x75 = 29.4960643587042
x76 = -39.9680398706701
x77 = -89.884456477708
x78 = 73.1292956585624
x79 = -211.359372416513
x80 = 86.0447321233204
x81 = 88.1391272257137
x82 = -58.46852994181
x83 = -8.20304748437335
x84 = 58.46852994181
x85 = 91.9788515801012
x86 = 8.20304748437335
x87 = -98.2620368872808
x88 = 39.9680398706701
x89 = 64.7517152489896
x90 = -100.356431989674
x91 = 62.6573201465964
x92 = 16.929693744345
x93 = 46.2512251778497
x94 = -54.2797397370236
x95 = -56.3741348394168
x96 = 47.9965544298441
x97 = -69.2895713041749
x97 = -69.2895713041749