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- La ecuación:
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Ecuación (|x|)=-2
- Ecuación -(1/5)*x^2+45=0
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Ecuación (x+2)(2x-8)-14=0
- Ecuación 16*y^2-49=0
- Expresar {x} en función de y en la ecuación:
- -17*x+9*y=-18
- -19*x-4*y=5
- -8*x-1*y=9
- 4*x+4*y=13
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Expresiones idénticas
- sin(treinta)*sin(x- treinta)-cos(sesenta)*cos(sesenta)= cero
- seno de (30) multiplicar por seno de (x menos 30) menos coseno de (60) multiplicar por coseno de (60) es igual a 0
- seno de (treinta) multiplicar por seno de (x menos treinta) menos coseno de (sesenta) multiplicar por coseno de (sesenta) es igual a cero
- sin(30)sin(x-30)-cos(60)cos(60)=0
- sin30sinx-30-cos60cos60=0
- sin(30)*sin(x-30)-cos(60)*cos(60)=O
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Expresiones semejantes
- sin(30)*sin(x-30)+cos(60)*cos(60)=0
- sin(30)*sin(x+30)-cos(60)*cos(60)=0
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Expresiones con funciones
- Seno sin
- sin(a)^(2)=1/2
- sin(2*a)/cos(a)=sin(a)
- sin(pi/2+x)-1/2=0
- sin(x/2)
- sin((3/2)x)=1
- Seno sin
- sin(a)^(2)=1/2
- sin(2*a)/cos(a)=sin(a)
- sin(pi/2+x)-1/2=0
- sin(x/2)
- sin((3/2)x)=1
sin(30)*sin(x-30)-cos(60)*cos(60)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
sin(30)*sin(x - 30) - cos(60)*cos(60) = 0
$$\sin{\left(30 \right)} \sin{\left(x - 30 \right)} - \cos{\left(60 \right)} \cos{\left(60 \right)} = 0$$
Solución detallada
Tenemos la ecuación
$$\sin{\left(30 \right)} \sin{\left(x - 30 \right)} - \cos{\left(60 \right)} \cos{\left(60 \right)} = 0$$
es la ecuación trigonométrica más simple
Obtenemos:
$$\sin{\left(30 \right)} \sin{\left(x - 30 \right)} - \cos{\left(60 \right)} \cos{\left(60 \right)} + \cos^{2}{\left(60 \right)} = \cos^{2}{\left(60 \right)}$$
La ecuación se convierte en
$$\sin{\left(x - 30 \right)} = \frac{\cos^{2}{\left(60 \right)}}{\sin{\left(30 \right)}}$$
Esta ecuación se reorganiza en
$$x - 30 = 2 \pi n + \operatorname{asin}{\left(\frac{\cos^{2}{\left(60 \right)}}{\sin{\left(30 \right)}} \right)}$$
$$x - 30 = 2 \pi n - \operatorname{asin}{\left(\frac{\cos^{2}{\left(60 \right)}}{\sin{\left(30 \right)}} \right)} + \pi$$
O
$$x - 30 = 2 \pi n + \operatorname{asin}{\left(\frac{\cos^{2}{\left(60 \right)}}{\sin{\left(30 \right)}} \right)}$$
$$x - 30 = 2 \pi n - \operatorname{asin}{\left(\frac{\cos^{2}{\left(60 \right)}}{\sin{\left(30 \right)}} \right)} + \pi$$
, donde n es cualquier número entero
Transportemos
$$-30$$
al miembro derecho de la ecuación
con el signo opuesto, en total:
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{\cos^{2}{\left(60 \right)}}{\sin{\left(30 \right)}} \right)} + 30$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{\cos^{2}{\left(60 \right)}}{\sin{\left(30 \right)}} \right)} + \pi + 30$$
$$\sin{\left(30 \right)} \sin{\left(x - 30 \right)} - \cos{\left(60 \right)} \cos{\left(60 \right)} = 0$$
es la ecuación trigonométrica más simple
Transportemos -cos(60)^2 al miembro derecho de la ecuación
cambiando el signo de -cos(60)^2
Obtenemos:
$$\sin{\left(30 \right)} \sin{\left(x - 30 \right)} - \cos{\left(60 \right)} \cos{\left(60 \right)} + \cos^{2}{\left(60 \right)} = \cos^{2}{\left(60 \right)}$$
Dividamos ambos miembros de la ecuación en sin(30)
La ecuación se convierte en
$$\sin{\left(x - 30 \right)} = \frac{\cos^{2}{\left(60 \right)}}{\sin{\left(30 \right)}}$$
Esta ecuación se reorganiza en
$$x - 30 = 2 \pi n + \operatorname{asin}{\left(\frac{\cos^{2}{\left(60 \right)}}{\sin{\left(30 \right)}} \right)}$$
$$x - 30 = 2 \pi n - \operatorname{asin}{\left(\frac{\cos^{2}{\left(60 \right)}}{\sin{\left(30 \right)}} \right)} + \pi$$
O
$$x - 30 = 2 \pi n + \operatorname{asin}{\left(\frac{\cos^{2}{\left(60 \right)}}{\sin{\left(30 \right)}} \right)}$$
$$x - 30 = 2 \pi n - \operatorname{asin}{\left(\frac{\cos^{2}{\left(60 \right)}}{\sin{\left(30 \right)}} \right)} + \pi$$
, donde n es cualquier número entero
Transportemos
$$-30$$
al miembro derecho de la ecuación
con el signo opuesto, en total:
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{\cos^{2}{\left(60 \right)}}{\sin{\left(30 \right)}} \right)} + 30$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{\cos^{2}{\left(60 \right)}}{\sin{\left(30 \right)}} \right)} + \pi + 30$$
Respuesta rápida
[src]
/ 2 \
|cos (60)|
x1 = 30 + asin|--------|
\sin(30) /
$$x_{1} = \operatorname{asin}{\left(\frac{\cos^{2}{\left(60 \right)}}{\sin{\left(30 \right)}} \right)} + 30$$
/ 2 \
|cos (60)|
x2 = 30 + pi - asin|--------|
\sin(30) /
$$x_{2} = - \operatorname{asin}{\left(\frac{\cos^{2}{\left(60 \right)}}{\sin{\left(30 \right)}} \right)} + \pi + 30$$
x2 = -asin(cos(60)^2/sin(30)) + pi + 30
Suma y producto de raíces
[src]
suma
/ 2 \ / 2 \
|cos (60)| |cos (60)|
30 + asin|--------| + 30 + pi - asin|--------|
\sin(30) / \sin(30) /
$$\left(\operatorname{asin}{\left(\frac{\cos^{2}{\left(60 \right)}}{\sin{\left(30 \right)}} \right)} + 30\right) + \left(- \operatorname{asin}{\left(\frac{\cos^{2}{\left(60 \right)}}{\sin{\left(30 \right)}} \right)} + \pi + 30\right)$$
=
60 + pi
$$\pi + 60$$
producto
/ / 2 \\ / / 2 \\ | |cos (60)|| | |cos (60)|| |30 + asin|--------||*|30 + pi - asin|--------|| \ \sin(30) // \ \sin(30) //
$$\left(\operatorname{asin}{\left(\frac{\cos^{2}{\left(60 \right)}}{\sin{\left(30 \right)}} \right)} + 30\right) \left(- \operatorname{asin}{\left(\frac{\cos^{2}{\left(60 \right)}}{\sin{\left(30 \right)}} \right)} + \pi + 30\right)$$
=
/ / 2 \\ / / 2 \\ | |cos (60)|| | |cos (60)|| |30 + asin|--------||*|30 + pi - asin|--------|| \ \sin(30) // \ \sin(30) //
$$\left(\operatorname{asin}{\left(\frac{\cos^{2}{\left(60 \right)}}{\sin{\left(30 \right)}} \right)} + 30\right) \left(- \operatorname{asin}{\left(\frac{\cos^{2}{\left(60 \right)}}{\sin{\left(30 \right)}} \right)} + \pi + 30\right)$$
(30 + asin(cos(60)^2/sin(30)))*(30 + pi - asin(cos(60)^2/sin(30)))
Respuesta numérica
[src]
x1 = -41.0934257512484
x2 = 84.5702803923433
x3 = 16.270424104324
x4 = 511.826881280555
x5 = 21.7384273205475
x6 = 90.8534656995229
x7 = -91.3589082086851
x8 = 34.3047979349067
x9 = -59.1277995818311
x10 = 47.6863506402219
x11 = -84.2605408105494
x12 = 41.4031653330423
x13 = -21.4286877387535
x14 = 28.8367947186831
x15 = -34.8102404440688
x16 = -65.4109848890106
x17 = -66.2261669799667
x18 = 97.9518330976586
x19 = 91.668647790479
x20 = 78.2870950851638
x21 = 273.065839607731
x22 = 2.88887139900872
x23 = 53.9695359474015
x24 = 65.7207244708046
x25 = -1435.14538185416
x26 = 72.8190918689402
x27 = 59.437539163625
x28 = 79.1022771761198
x29 = -15.145502431574
x30 = -53.6597963656076
x31 = 28.0216126277271
x32 = -147.907575973301
x33 = 3.7040534899648
x34 = -15251.8698723421
x35 = -59.9429816727871
x36 = -8.86231712439437
x37 = 35.1199800258627
x38 = 97.1366510067025
x39 = 40.5879832420862
x40 = 60.2527212545811
x41 = -71.6941701961902
x42 = -2.57913181721479
x43 = -78.7925375943259
x44 = -90.543726117729
x45 = 9873.77298897814
x46 = 15.4552420133679
x47 = -40.2782436602923
x48 = 22.5536094115036
x49 = -9.67749921535046
x50 = -33.9950583531127
x51 = -72.5093522871463
x52 = -15.96068452253
x53 = 66.5359065617607
x54 = -681.16314499261
x55 = 9.1720567061883
x56 = 85.3854624832994
x57 = 72.0039097779842
x58 = -27.7118730459331
x59 = -85.0757229015055
x60 = -28.5270551368892
x61 = -52.8446142746515
x62 = 53.1543538564454
x63 = -47.376611058428
x64 = -77.9773555033698
x65 = -22.2438698297096
x66 = -46.5614289674719
x67 = 46.8711685492658
x68 = -96.8269114249086
x69 = 9.98723879714439
x70 = -3.39431390817087
x71 = -97.6420935158647
x71 = -97.6420935158647