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- La ecuación:
-
Ecuación 3^x+4^x=5^x
-
Ecuación (x-2)^4+3*(x-2)^2-10=0
-
Ecuación x+2/x=3
-
Ecuación x^2=-2
- Expresar {x} en función de y en la ecuación:
- -9*x-15*y=-4
- -13*x+7*y=11
- -7*x-7*y=-14
- 2*x+13*y=19
- Integral de d{x}:
- sin4x
- Derivada de:
-
sin4x
- Gráfico de la función y =:
- sin4x
-
Expresiones idénticas
- sin4x=-((sqrt dos)/2)
- seno de 4x es igual a menos (( raíz cuadrada de 2) dividir por 2)
- seno de 4x es igual a menos (( raíz cuadrada de dos) dividir por 2)
- sin4x=-((√2)/2)
- sin4x=-sqrt2/2
- sin4x=-((sqrt2) dividir por 2)
-
Expresiones semejantes
- arccos((7x+5)/13)=arcsin((4x+1)/13)
- sin^4(x)=cos^4(x)-cos(2*x)=0,5
- sin(3*x)-sin(4*x)+sin(5*x)=0
- cos(x/2)=-sqrt2/2
- sin(x)=-(sqrt2/2)
- cos(x)=-(sqrt(2)/2)
- sin4x=+((sqrt2)/2)
- sin(x)=-(sqrt(2)/2)
- cos(8*x)+7*sin(4*x)-6=0
sin4x=-((sqrt2)/2) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
___
-\/ 2
sin(4*x) = -------
2
$$\sin{\left(4 x \right)} = - \frac{\sqrt{2}}{2}$$
Solución detallada
Tenemos la ecuación
$$\sin{\left(4 x \right)} = - \frac{\sqrt{2}}{2}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$4 x = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{2}}{2} \right)}$$
$$4 x = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{2}}{2} \right)} + \pi$$
O
$$4 x = 2 \pi n - \frac{\pi}{4}$$
$$4 x = 2 \pi n + \frac{5 \pi}{4}$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$4$$
obtenemos la respuesta:
$$x_{1} = \frac{\pi n}{2} - \frac{\pi}{16}$$
$$x_{2} = \frac{\pi n}{2} + \frac{5 \pi}{16}$$
$$\sin{\left(4 x \right)} = - \frac{\sqrt{2}}{2}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$4 x = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{2}}{2} \right)}$$
$$4 x = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{2}}{2} \right)} + \pi$$
O
$$4 x = 2 \pi n - \frac{\pi}{4}$$
$$4 x = 2 \pi n + \frac{5 \pi}{4}$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$4$$
obtenemos la respuesta:
$$x_{1} = \frac{\pi n}{2} - \frac{\pi}{16}$$
$$x_{2} = \frac{\pi n}{2} + \frac{5 \pi}{16}$$
Suma y producto de raíces
[src]
suma
pi 5*pi - -- + ---- 16 16
$$- \frac{\pi}{16} + \frac{5 \pi}{16}$$
=
pi -- 4
$$\frac{\pi}{4}$$
producto
-pi 5*pi ----*---- 16 16
$$- \frac{\pi}{16} \frac{5 \pi}{16}$$
=
2 -5*pi ------ 256
$$- \frac{5 \pi^{2}}{256}$$
-5*pi^2/256
Respuesta rápida
[src]
-pi
x1 = ----
16
$$x_{1} = - \frac{\pi}{16}$$
5*pi
x2 = ----
16
$$x_{2} = \frac{5 \pi}{16}$$
x2 = 5*pi/16
Respuesta numérica
[src]
x1 = 4.1233403578366
x2 = -99.5492172106266
x3 = 46.5348411812988
x4 = -69.7040870015235
x5 = 10.4065256650162
x6 = 32.3976742401447
x7 = 51.2472301616835
x8 = -63.0282026126452
x9 = -77.558068635498
x10 = 84.2339530243763
x11 = -58.3158136322605
x12 = 6.08683576633022
x13 = -19.4386045440868
x14 = 35.9319659754333
x15 = 65.7770961845363
x16 = -97.9784208838317
x17 = 84.6266521060751
x18 = -14.7262155637022
x19 = 70.0967860832223
x20 = -91.6952355766521
x21 = -94.4441291485432
x22 = -47.712938426395
x23 = -37.8954613839269
x24 = 48.1056375080937
x25 = 11.9773219918111
x26 = 94.0514300668444
x27 = -81.877758534184
x28 = 43.7859476094077
x29 = 13.9408174003047
x30 = -52.0326283250809
x31 = -75.9872723087031
x32 = 24.5436926061703
x33 = 26.1144889329652
x34 = 54.3888228152733
x35 = -23.7582944427728
x36 = -88.1609438413636
x37 = 197.723987635308
x38 = 68.5259897564274
x39 = 62.2428044492478
x40 = -74.0237769002095
x41 = 72.0602814917159
x42 = -59.8866099590554
x43 = 2.55254403104171
x44 = -10.0138265833175
x45 = 92.0879346583508
x46 = 86.1974484328699
x47 = -17.8678082172919
x48 = -53.9961237335746
x49 = -44.1786466911065
x50 = -61.8501053675491
x51 = -15.9043128087983
x52 = 64.2062998577414
x53 = 99.9419162923253
x54 = 109.366694253095
x55 = -25.7217898512664
x56 = 33.9684705669396
x57 = -90.1244392498572
x58 = 79.9142631256904
x59 = 21.7947990342792
x60 = -85.0193511877738
x61 = 29.2560815865549
x62 = -89.7317401681585
x63 = -66.169795266235
x64 = -80.3069622073891
x65 = -11.5846229101124
x66 = 57.9231145505618
x67 = -83.8412539426776
x68 = 77.9507677171967
x69 = -3.73064127613788
x70 = -33.5757714852409
x71 = 90.5171383315559
x72 = -45.7494430179014
x73 = -1.76714586764426
x74 = 87.7682447596649
x75 = 76.3799713904018
x76 = -67.7405915930299
x77 = 50.0691329165873
x78 = 42.2151512826128
x79 = 20.2240027074843
x80 = -96.0149254753381
x81 = 55.9596191420682
x82 = -32.004975158446
x83 = -30.0414797499524
x84 = -0.196349540849362
x85 = 227.176418762712
x86 = -36.7173641388307
x87 = 28.0779843414588
x88 = 40.2516558741192
x89 = -8.05033117482385
x90 = 62.6355035309465
x91 = 98.3711199655304
x92 = -22.1874981159779
x93 = 18.2605072989907
x94 = 7.2649330114264
x95 = -39.8589567924205
x96 = -55.5669200603695
x96 = -55.5669200603695