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- La ecuación:
-
Ecuación x^4+2*x^2-8=0
-
Ecuación x*(x^2+8*x+16)=5*(x+4)
-
Ecuación -25-x=-17
-
Ecuación x^2+3x=4
- Expresar {x} en función de y en la ecuación:
- -18*x-2*y=9
- -14*x+10*y=19
- -9*x+1*y=3
- -17*x+1*y=-11
- Derivada de:
-
sin(3x)
- Integral de d{x}:
- sin(3x)
- Forma canónica:
- sin(3x)
-
Expresiones idénticas
- sin(3x)=-sqrt3/ dos
- seno de (3x) es igual a menos raíz cuadrada de 3 dividir por 2
- seno de (3x) es igual a menos raíz cuadrada de 3 dividir por dos
- sin(3x)=-√3/2
- sin3x=-sqrt3/2
- sin(3x)=-sqrt3 dividir por 2
-
Expresiones semejantes
- sin(3*x)=-1/2
- sin3x+sinx-sin2x=2cos^2x-2cosx
- sin3x=0
- \sin(x)=-sqrt(3)/2
- sin(3x)=+sqrt3/2
- cos(x/7)=-sqrt(3)/2
- 1+sin6x=(sin3x-cos3x)2
- sin(3*x)=-1
- sin(x)+sqrt(((2-sqrt(3))/2)(cos(x)+1))=0
-
Expresiones con funciones
- Seno sin
- sin(x)=1,5
- sin(x-1)=0
- sin2x=1
- sin(3*x)=-1/2
- sin(3*x)=-1
sin(3x)=-sqrt3/2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
___
-\/ 3
sin(3*x) = -------
2
$$\sin{\left(3 x \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
Solución detallada
Tenemos la ecuación
$$\sin{\left(3 x \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$3 x = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)}$$
$$3 x = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)} + \pi$$
O
$$3 x = 2 \pi n - \frac{\pi}{3}$$
$$3 x = 2 \pi n + \frac{4 \pi}{3}$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$3$$
obtenemos la respuesta:
$$x_{1} = \frac{2 \pi n}{3} - \frac{\pi}{9}$$
$$x_{2} = \frac{2 \pi n}{3} + \frac{4 \pi}{9}$$
$$\sin{\left(3 x \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$3 x = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)}$$
$$3 x = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)} + \pi$$
O
$$3 x = 2 \pi n - \frac{\pi}{3}$$
$$3 x = 2 \pi n + \frac{4 \pi}{3}$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$3$$
obtenemos la respuesta:
$$x_{1} = \frac{2 \pi n}{3} - \frac{\pi}{9}$$
$$x_{2} = \frac{2 \pi n}{3} + \frac{4 \pi}{9}$$
Suma y producto de raíces
[src]
suma
pi 4*pi - -- + ---- 9 9
$$- \frac{\pi}{9} + \frac{4 \pi}{9}$$
=
pi -- 3
$$\frac{\pi}{3}$$
producto
-pi 4*pi ----*---- 9 9
$$- \frac{\pi}{9} \frac{4 \pi}{9}$$
=
2 -4*pi ------ 81
$$- \frac{4 \pi^{2}}{81}$$
-4*pi^2/81
Respuesta rápida
[src]
-pi
x1 = ----
9
$$x_{1} = - \frac{\pi}{9}$$
4*pi
x2 = ----
9
$$x_{2} = \frac{4 \pi}{9}$$
x2 = 4*pi/9
Respuesta numérica
[src]
x1 = -6.63225115757845
x2 = -63.5299847725936
x3 = 43.6332312998582
x4 = -469.493568786475
x5 = 68.4169066781777
x6 = 8.02851455917392
x7 = -17.4532925199433
x8 = -54.8033385126219
x9 = -86.2192650485199
x10 = 89.7099235525085
x11 = -69.8131700797732
x12 = 5.93411945678072
x13 = -13.2645023151569
x14 = 39.095375244673
x15 = 33.1612557878923
x16 = -75.7472895365539
x17 = 24.4346095279206
x18 = 100.181899064475
x19 = 18.151424220741
x20 = -19.1986217719376
x21 = -57.246799465414
x22 = -42.2369678982628
x23 = -90.4080552533063
x24 = -19.5476876223365
x25 = -88.3136601509131
x26 = 45.7276264022514
x27 = 66.6715774261834
x28 = -38.0481776934764
x29 = -2.44346095279206
x30 = 1.74532925199433
x31 = 72.6056968829641
x32 = -76.0963553869528
x33 = -30.0196631343025
x34 = -40.1425727958696
x35 = -33.85938748869
x36 = -56.8977336150151
x37 = -4.88692190558412
x38 = 95.9931088596881
x39 = -15.3588974175501
x40 = -10.8210413623648
x41 = 10.1229096615671
x42 = -31.7649923862968
x43 = 60.0393262686049
x44 = -21.2930168743308
x45 = 14.3116998663535
x46 = 62.1337213709981
x47 = 70.5113017805709
x48 = 47.8220215046446
x49 = 83.0776723949301
x50 = -84.1248699461267
x51 = -35.9537825910832
x52 = -74.0019602845596
x53 = -59.3411945678072
x54 = -46.4257581030492
x55 = 91.8043186549017
x56 = -82.0304748437335
x57 = -23.7364778271229
x58 = 93.8987137572949
x59 = -25.8308729295161
x60 = 26.5290046303138
x61 = 56.1996019142174
x62 = 54.1052068118242
x63 = 12.2173047639603
x64 = -27.9252680319093
x65 = 66.3225115757845
x66 = 52.010811709431
x67 = 28.623399732707
x68 = -46.774823953448
x69 = 22.3402144255274
x70 = 20.2458193231342
x71 = -79.9360797413403
x72 = -61.4355896702004
x73 = 16.0570291183478
x74 = -21.6420827247297
x75 = -77.8416846389471
x76 = -67.71877497738
x77 = 77.1435529381494
x78 = 3.83972435438753
x79 = -65.6243798749868
x80 = -44.331363000656
x81 = -92.5024503556995
x82 = 49.9164166070378
x83 = -126.361837844389
x84 = 64.2281164733913
x85 = 30.7177948351002
x86 = 41.538836197465
x87 = -71.9075651821664
x88 = 58.2939970166106
x89 = -94.9459113084915
x90 = 74.7000919853573
x91 = -50.6145483078356
x92 = -0.349065850398866
x93 = -49469.9613843777
x94 = 87.6155284501153
x95 = 85.5211333477222
x96 = 98.0875039620813
x96 = 98.0875039620813