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- La ecuación:
-
Ecuación 2x^2-x-1=x^2-5x-(-1-x^2)
-
Ecuación x^2+4=5x
-
Ecuación x(x^2+2x+1)=6(x+1)
-
Ecuación 4x+1=-3x+15
- Expresar {x} en función de y en la ecuación:
- -6*x-20*y=8
- 13*x-12*y=19
- -9*x+11*y=9
- -4*x-8*y=-20
- Derivada de:
-
cos(6x)
- Integral de d{x}:
- cos(6x)
- Gráfico de la función y =:
- cos(6x)
-
Expresiones idénticas
- cos(6x)=sqrt(dos)/ dos
- coseno de (6x) es igual a raíz cuadrada de (2) dividir por 2
- coseno de (6x) es igual a raíz cuadrada de (dos) dividir por dos
- cos(6x)=√(2)/2
- cos6x=sqrt2/2
- cos(6x)=sqrt(2) dividir por 2
-
Expresiones semejantes
- cos(6*x)-sin(x)=0
- sin(pi(x-3))/4=sqrt2/2
- 2-cos6x=1
- cos(2*x)+cos(8*x)-cos(6*x)=1
- f*(x)=3*cos(6*x)
-
Expresiones con funciones
- Coseno cos
- cos(x)=-(4/5)
- cos(x+(pi/6))=-1
- cos(3*x)=1
- cos(x)=-3/2
- cos(x)=1/2
- Raíz cuadrada sqrt
- sqrt(x-1)=x-3
- sqrt(x+6)=x
- sqrt(16-4*x)=2
- sqrt(12-x)=x
- sqrt(5/(15-x))=1
cos(6x)=sqrt(2)/2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Tenemos la ecuación
$$\cos{\left(6 x \right)} = \frac{\sqrt{2}}{2}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$6 x = \pi n + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$6 x = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
O
$$6 x = \pi n + \frac{\pi}{4}$$
$$6 x = \pi n - \frac{3 \pi}{4}$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$6$$
obtenemos la respuesta:
$$x_{1} = \frac{\pi n}{6} + \frac{\pi}{24}$$
$$x_{2} = \frac{\pi n}{6} - \frac{\pi}{8}$$
$$\cos{\left(6 x \right)} = \frac{\sqrt{2}}{2}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$6 x = \pi n + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$6 x = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
O
$$6 x = \pi n + \frac{\pi}{4}$$
$$6 x = \pi n - \frac{3 \pi}{4}$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$6$$
obtenemos la respuesta:
$$x_{1} = \frac{\pi n}{6} + \frac{\pi}{24}$$
$$x_{2} = \frac{\pi n}{6} - \frac{\pi}{8}$$
Respuesta rápida
[src]
pi
x1 = --
24
$$x_{1} = \frac{\pi}{24}$$
7*pi
x2 = ----
24
$$x_{2} = \frac{7 \pi}{24}$$
x2 = 7*pi/24
Suma y producto de raíces
[src]
suma
pi 7*pi -- + ---- 24 24
$$\frac{\pi}{24} + \frac{7 \pi}{24}$$
=
pi -- 3
$$\frac{\pi}{3}$$
producto
pi 7*pi --*---- 24 24
$$\frac{\pi}{24} \frac{7 \pi}{24}$$
=
2 7*pi ----- 576
$$\frac{7 \pi^{2}}{576}$$
7*pi^2/576
Respuesta numérica
[src]
x1 = 46.2075919465499
x2 = -19.7658537788358
x3 = -37.8300115369771
x4 = 48.3019870489431
x5 = 94.1168799137942
x6 = 0.130899693899575
x7 = 8.24668071567321
x8 = 26.3108384738145
x9 = -89.9280897090078
x10 = -9.29387826686981
x11 = -23.9546439836222
x12 = -28.1434341884086
x13 = 10.3410758180664
x14 = -83.9067037896274
x15 = -18.7186562276392
x16 = 72.1257313386657
x17 = 25.0018415348188
x18 = -57.7267650097125
x19 = -41.7570023539643
x20 = 88.0954939944138
x21 = 22.1220482690281
x22 = -33.6412213321907
x23 = 111.919238284136
x24 = 66.1043454192852
x25 = -63.7481509290929
x26 = 44.1131968441567
x27 = 54.3233729683235
x28 = -77.6235184824478
x29 = 30.2378292908018
x30 = 50.1345827635371
x31 = -15.8388629618485
x32 = 64.009950316892
x33 = 61.9155552144988
x34 = 81.550509299435
x35 = 100.661864608773
x36 = -79.717913584841
x37 = -70.0313362362725
x38 = 68.1987405216784
x39 = -110.086642569542
x40 = 76.3145215434521
x41 = -87.8336946066146
x42 = 74.2201264410589
x43 = 32.332224393195
x44 = 2.22529479629277
x45 = -6.15228561328001
x46 = -13.7444678594553
x47 = -90.9752872602044
x48 = 96.4730744039866
x49 = -94.1168799137942
x50 = -72.1257313386657
x51 = 42.0188017417635
x52 = -99.6146670575764
x53 = -61.9155552144988
x54 = -35.7356164345839
x55 = 28.1434341884086
x56 = -11.6500727570621
x57 = -81.8123086872342
x58 = 86.0010988920206
x59 = 52.2289778659303
x60 = -65.8425460314861
x61 = 58.773962560909
x62 = 78.4089166458453
x63 = 37.8300115369771
x64 = 83.9067037896274
x65 = 90.189889096807
x66 = 20.0276531666349
x67 = -45.9457925587507
x68 = -43.8513974563575
x69 = 15.8388629618485
x70 = -67.9369411338793
x71 = -92.022484811401
x72 = 22.9074464324256
x73 = -59.8211601121056
x74 = 70.2931356240716
x75 = 100.400065220974
x76 = 12.6972703082587
x77 = 6.15228561328001
x78 = 56.4177680707167
x79 = 24.2164433714213
x80 = 98.3056701185806
x81 = -1.96349540849362
x82 = 96.2112750161874
x83 = -50.1345827635371
x84 = -21.860248881229
x85 = -48.0401876611439
x86 = 39.9244066393703
x87 = -86.0010988920206
x88 = 92.2842841992002
x89 = 5.36688744988256
x90 = -55.6323699073193
x91 = 17.9332580642417
x92 = -26.0490390860154
x93 = -31.2850268419984
x94 = 10.6028752058656
x95 = -4.05789051088682
x95 = -4.05789051088682