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- La ecuación:
-
Ecuación x=(x+1)/2
- Ecuación (x-6)(-5x-9)=0
-
Ecuación x^2-14*x+33=0
-
Ecuación x^2-5x=14
- Expresar {x} en función de y en la ecuación:
- 12*x+1*y=15
- -17*x-12*y=-9
- 18*x+17*y=-14
- 16*x-17*y=-15
- Integral de d{x}:
- cos(5x)
- Derivada de:
-
cos(5x)
- Suma de la serie:
- cos(5x)
-
Expresiones idénticas
- cos(5x)=√ dos / dos
- coseno de (5x) es igual a √2 dividir por 2
- coseno de (5x) es igual a √ dos dividir por dos
- cos5x=√2/2
- cos(5x)=√2 dividir por 2
-
Expresiones semejantes
- f*(x)=cos(5*x-3)
- cos(5*x)^2=4
- 2*cos(5*x)=0
- f*x=(sin(5*x)+cos(5*x))^3
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Expresiones con funciones
- Coseno cos
- cos(x)^(2)=cos(x)
- cos^2(x-1)=0
- cosπ(2x+30)/4=-√2/2
- cos^2(x/4)-sin^2(x/4)=sin((3pi/2)-x)
- cos((пи/2)+x)=cos(пи/6)
cos(5x)=√2/2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Tenemos la ecuación
$$\cos{\left(5 x \right)} = \frac{\sqrt{2}}{2}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$5 x = \pi n + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$5 x = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
O
$$5 x = \pi n + \frac{\pi}{4}$$
$$5 x = \pi n - \frac{3 \pi}{4}$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$5$$
obtenemos la respuesta:
$$x_{1} = \frac{\pi n}{5} + \frac{\pi}{20}$$
$$x_{2} = \frac{\pi n}{5} - \frac{3 \pi}{20}$$
$$\cos{\left(5 x \right)} = \frac{\sqrt{2}}{2}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$5 x = \pi n + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$5 x = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
O
$$5 x = \pi n + \frac{\pi}{4}$$
$$5 x = \pi n - \frac{3 \pi}{4}$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$5$$
obtenemos la respuesta:
$$x_{1} = \frac{\pi n}{5} + \frac{\pi}{20}$$
$$x_{2} = \frac{\pi n}{5} - \frac{3 \pi}{20}$$
Suma y producto de raíces
[src]
suma
pi 7*pi -- + ---- 20 20
$$\frac{\pi}{20} + \frac{7 \pi}{20}$$
=
2*pi ---- 5
$$\frac{2 \pi}{5}$$
producto
pi 7*pi --*---- 20 20
$$\frac{\pi}{20} \frac{7 \pi}{20}$$
=
2 7*pi ----- 400
$$\frac{7 \pi^{2}}{400}$$
7*pi^2/400
Respuesta rápida
[src]
pi
x1 = --
20
$$x_{1} = \frac{\pi}{20}$$
7*pi
x2 = ----
20
$$x_{2} = \frac{7 \pi}{20}$$
x2 = 7*pi/20
Respuesta numérica
[src]
x1 = -27.8030949842697
x2 = -30.0022098417825
x3 = -79.0110552377833
x4 = 16.1792021659874
x5 = -50.1084028247572
x6 = -40.0553063332699
x7 = 32.8296432300133
x8 = 88.1216739331937
x9 = 27.8030949842697
x10 = -94.0906999750143
x11 = 84.037603483527
x12 = 54.1924732744239
x13 = -16.1792021659874
x14 = -57.9623844587317
x15 = 202.475646523862
x16 = -97.8606111593221
x17 = 73.9845069920396
x18 = -17.7499984927823
x19 = -71.7853921345268
x20 = 57.9623844587317
x21 = 100.373885282194
x22 = -73.9845069920396
x23 = -87.8075146678347
x24 = -61.7322956430394
x25 = -47.9092879672443
x26 = 90.3207887907066
x27 = -21.5199096770901
x28 = 30.0022098417825
x29 = 61.4181363776805
x30 = -15.2367243699105
x31 = -84.037603483527
x32 = -9.89601685880785
x33 = -95.6614963018092
x34 = 66.4446846234241
x35 = -60.1614993162445
x36 = -81.8384886260141
x37 = 68.015480950219
x38 = -3.92699081698724
x39 = -70.2145958077319
x40 = -75.5553033188345
x41 = 37.856191475757
x42 = -53.878314009065
x43 = -6.1261056745001
x44 = -65.1880475619882
x45 = 22.462387473167
x46 = -77.7544181763474
x47 = 47.9092879672443
x48 = 36.2853951489621
x49 = 91.8915851175014
x50 = -19.9491133502952
x51 = 34.0862802914493
x52 = 26.2322986574748
x53 = 20.2632726156542
x54 = 71.7853921345268
x55 = 24.0331837999619
x56 = 50.1084028247572
x57 = 40.0553063332699
x58 = 81.8384886260141
x59 = -80.5818515645782
x60 = 98.174770424681
x61 = 10.2101761241668
x62 = 76.8119403802704
x63 = -13.9800873084746
x64 = -7.69690200129499
x65 = -31.5730061685774
x66 = -51.6791991515521
x67 = 96.9181333632451
x68 = -68.015480950219
x69 = 44.1393767829366
x70 = -37.856191475757
x71 = -33.7721210260903
x72 = 3.92699081698724
x73 = -41.6261026600648
x74 = 0.15707963267949
x75 = -85.6083998103219
x76 = -525.117212047534
x77 = 17.4358392274234
x78 = -42.8827397215007
x79 = 56.3915881319368
x80 = -43.8252175175776
x81 = -63.9314105005523
x82 = 89.3783109946296
x83 = 94.0906999750143
x84 = 64.2455697659113
x85 = 78.0685774417064
x86 = 6.1261056745001
x87 = 80.2676922992192
x88 = 46.3384916404494
x89 = 13.9800873084746
x90 = 12.4092909816797
x91 = -91.8915851175014
x92 = 11.1526539202438
x93 = 70.2145958077319
x94 = 60.1614993162445
x95 = 2.35619449019234
x95 = 2.35619449019234