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- La ecuación:
-
Ecuación x^2-5x-14=0
-
Ecuación (x-9)^3+3*(x-9)^2=0
-
Ecuación 2x²-18=0
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Ecuación cos(3x)=sqrt(3)/2
- Expresar {x} en función de y en la ecuación:
- -20*x-18*y=-11
- -6*x-17*y=14
- 15*x+14*y=19
- 5*x-2*y=-14
- Integral de d{x}:
- cos(3x)
- Derivada de:
-
cos(3x)
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sqrt(3)/2
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Expresiones idénticas
- cos(tres x)=sqrt(3)/ dos
- coseno de (3x) es igual a raíz cuadrada de (3) dividir por 2
- coseno de (tres x) es igual a raíz cuadrada de (3) dividir por dos
- cos(3x)=√(3)/2
- cos3x=sqrt3/2
- cos(3x)=sqrt(3) dividir por 2
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Expresiones semejantes
- sin(3*x-pi/6)=(-sqrt(3))/2
- cos3x=-1
- 4sqrt((1-((sqrt(3))/2))/(6x+6))+pi/(6x+6)=1,5*sqrt(3)-2
- cos3x=1/2
- cos2x*sin3x-sin2x*cos3x=1
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Expresiones con funciones
- Coseno cos
- cos(2x)+cos(x)=0
- cos(3x)=-1/2
- cosx=√2/2
- cos^2x+3cosx=0
- cos^2x=3/4
- Raíz cuadrada sqrt
- sqrt(9a^2-b^2)
- sqrt(x)=7.89
- sqrt(x^2-36)=8
- sqrt(5x^2-20x+21)+sqrt(3x^2-12x+28)=8x-2x^2-3
- sqrt(2+log2(x))=log2(x)
cos(3x)=sqrt(3)/2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Tenemos la ecuación
$$\cos{\left(3 x \right)} = \frac{\sqrt{3}}{2}$$
es la ecuación trigonométrica más simple
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:
$$x_{1} = \frac{\pi n}{3} + \frac{\pi}{18}$$
$$x_{2} = \frac{\pi n}{3} - \frac{5 \pi}{18}$$
$$\cos{\left(3 x \right)} = \frac{\sqrt{3}}{2}$$
es la ecuación trigonométrica más simple
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:
$$x_{1} = \frac{\pi n}{3} + \frac{\pi}{18}$$
$$x_{2} = \frac{\pi n}{3} - \frac{5 \pi}{18}$$
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 rápida
[src]
pi
x1 = --
18
$$x_{1} = \frac{\pi}{18}$$
11*pi
x2 = -----
18
$$x_{2} = \frac{11 \pi}{18}$$
x2 = 11*pi/18
Respuesta numérica
[src]
x1 = -94.0732466824944
x2 = -6.10865238198015
x3 = 29.1469985083053
x4 = -16.929693744345
x5 = 27.0526034059121
x6 = 2.26892802759263
x7 = 94.0732466824944
x8 = 16.929693744345
x9 = -77.6671517137477
x10 = -54.2797397370236
x11 = -22.8638132011257
x12 = -60.9119908946021
x13 = -12.3918376891597
x14 = 91.9788515801012
x15 = 64.7517152489896
x16 = -100.356431989674
x17 = -69.2895713041749
x18 = 73.1292956585624
x19 = 79.7615468161409
x20 = -39.9680398706701
x21 = 67.1951762017817
x22 = -1.91986217719376
x23 = 35.7792496658838
x24 = -29.4960643587042
x25 = 47.9965544298441
x26 = -91.9788515801012
x27 = -20.7694180987325
x28 = 42.0624349730633
x29 = -96.1676417848876
x30 = -81.5068760681352
x31 = -4.01425727958696
x32 = -81.8559419185341
x33 = 60.5629250442032
x34 = 96.1676417848876
x35 = 46.2512251778497
x36 = 4.01425727958696
x37 = -73.4783615089613
x38 = 16.5806278939461
x39 = -86.0447321233204
x40 = -79.7615468161409
x41 = 18.6750229963393
x42 = 10.2974425867665
x43 = -52.1853446346305
x44 = 29.4960643587042
x45 = -98.2620368872808
x46 = 33.6848545634906
x47 = 6.10865238198015
x48 = -27.401669256311
x49 = -31.5904594610974
x50 = 98.2620368872808
x51 = 14.4862327915529
x52 = 25.3072741539178
x53 = -83.9503370209273
x54 = -66.8461103513828
x55 = 56.3741348394168
x56 = 31.5904594610974
x57 = 58.46852994181
x58 = 54.2797397370236
x59 = -75.5727566113545
x60 = 75.5727566113545
x61 = -47.9965544298441
x62 = 44.1568300754565
x63 = -50.0909495322373
x64 = -41.7133691226645
x65 = -71.3839664065681
x66 = 83.9503370209273
x67 = -89.884456477708
x68 = 90.2335223281068
x69 = 50.0909495322373
x70 = -211.359372416513
x71 = -10.6465084371654
x72 = 81.8559419185341
x73 = 86.0447321233204
x74 = 100.705497840073
x75 = -8.20304748437335
x76 = -45.9021593274509
x77 = 88.1391272257137
x78 = -10.2974425867665
x79 = 77.6671517137477
x80 = -87.7900613753148
x81 = -35.7792496658838
x82 = -43.8077642250577
x83 = 100.356431989674
x84 = 12.3918376891597
x85 = -25.3072741539178
x86 = 8.20304748437335
x87 = 0.174532925199433
x88 = -79.412480965742
x89 = 39.9680398706701
x90 = -56.3741348394168
x91 = -14.4862327915529
x92 = 62.6573201465964
x93 = -58.46852994181
x94 = -33.6848545634906
x95 = -37.873644768277
x96 = 52.1853446346305
x97 = 37.873644768277
x97 = 37.873644768277
Gráfico