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Ecuación x^2-14*x+33=0
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Ecuación 5-x^2=0
- Expresar {x} en función de y en la ecuación:
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Expresiones idénticas
- SIN(x)^ dos + uno / treinta *SIN(x)- uno / treinta = cero
- SIN(x) al cuadrado más 1 dividir por 30 multiplicar por SIN(x) menos 1 dividir por 30 es igual a 0
- SIN(x) en el grado dos más uno dividir por treinta multiplicar por SIN(x) menos uno dividir por treinta es igual a cero
- SIN(x)2+1/30*SIN(x)-1/30=0
- SINx2+1/30*SINx-1/30=0
- SIN(x)²+1/30*SIN(x)-1/30=0
- SIN(x) en el grado 2+1/30*SIN(x)-1/30=0
- SIN(x)^2+1/30SIN(x)-1/30=0
- SIN(x)2+1/30SIN(x)-1/30=0
- SINx2+1/30SINx-1/30=0
- SINx^2+1/30SINx-1/30=0
- SIN(x)^2+1/30*SIN(x)-1/30=O
- SIN(x)^2+1 dividir por 30*SIN(x)-1 dividir por 30=0
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Expresiones semejantes
- SIN(x)^2+1/30*SIN(x)+1/30=0
- SIN(x)^2-1/30*SIN(x)-1/30=0
SIN(x)^2+1/30*SIN(x)-1/30=0 la ecuación
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Solución
Ha introducido
[src]
2 sin(x) 1
sin (x) + ------ - -- = 0
30 30
$$\left(\sin^{2}{\left(x \right)} + \frac{\sin{\left(x \right)}}{30}\right) - \frac{1}{30} = 0$$
Solución detallada
Tenemos la ecuación
$$\left(\sin^{2}{\left(x \right)} + \frac{\sin{\left(x \right)}}{30}\right) - \frac{1}{30} = 0$$
cambiamos
$$\sin^{2}{\left(x \right)} + \frac{\sin{\left(x \right)}}{30} - \frac{1}{30} = 0$$
$$\left(\sin^{2}{\left(x \right)} + \frac{\sin{\left(x \right)}}{30}\right) - \frac{1}{30} = 0$$
Sustituimos
$$w = \sin{\left(x \right)}$$
Es la ecuación de la forma
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$w_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$w_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = 1$$
$$b = \frac{1}{30}$$
$$c = - \frac{1}{30}$$
, entonces
Como D > 0 la ecuación tiene dos raíces.
o
$$w_{1} = \frac{1}{6}$$
$$w_{2} = - \frac{1}{5}$$
hacemos cambio inverso
$$\sin{\left(x \right)} = w$$
Tenemos la ecuación
$$\sin{\left(x \right)} = w$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
O
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
, donde n es cualquier número entero
sustituimos w:
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(w_{1} \right)}$$
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(\frac{1}{6} \right)}$$
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(\frac{1}{6} \right)}$$
$$x_{2} = 2 \pi n + \operatorname{asin}{\left(w_{2} \right)}$$
$$x_{2} = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{5} \right)}$$
$$x_{2} = 2 \pi n - \operatorname{asin}{\left(\frac{1}{5} \right)}$$
$$x_{3} = 2 \pi n - \operatorname{asin}{\left(w_{1} \right)} + \pi$$
$$x_{3} = 2 \pi n - \operatorname{asin}{\left(\frac{1}{6} \right)} + \pi$$
$$x_{3} = 2 \pi n - \operatorname{asin}{\left(\frac{1}{6} \right)} + \pi$$
$$x_{4} = 2 \pi n - \operatorname{asin}{\left(w_{2} \right)} + \pi$$
$$x_{4} = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{5} \right)} + \pi$$
$$x_{4} = 2 \pi n + \operatorname{asin}{\left(\frac{1}{5} \right)} + \pi$$
$$\left(\sin^{2}{\left(x \right)} + \frac{\sin{\left(x \right)}}{30}\right) - \frac{1}{30} = 0$$
cambiamos
$$\sin^{2}{\left(x \right)} + \frac{\sin{\left(x \right)}}{30} - \frac{1}{30} = 0$$
$$\left(\sin^{2}{\left(x \right)} + \frac{\sin{\left(x \right)}}{30}\right) - \frac{1}{30} = 0$$
Sustituimos
$$w = \sin{\left(x \right)}$$
Es la ecuación de la forma
a*w^2 + b*w + c = 0
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$w_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$w_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = 1$$
$$b = \frac{1}{30}$$
$$c = - \frac{1}{30}$$
, entonces
D = b^2 - 4 * a * c =
(1/30)^2 - 4 * (1) * (-1/30) = 121/900
Como D > 0 la ecuación tiene dos raíces.
w1 = (-b + sqrt(D)) / (2*a)
w2 = (-b - sqrt(D)) / (2*a)
o
$$w_{1} = \frac{1}{6}$$
$$w_{2} = - \frac{1}{5}$$
hacemos cambio inverso
$$\sin{\left(x \right)} = w$$
Tenemos la ecuación
$$\sin{\left(x \right)} = w$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
O
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
, donde n es cualquier número entero
sustituimos w:
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(w_{1} \right)}$$
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(\frac{1}{6} \right)}$$
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(\frac{1}{6} \right)}$$
$$x_{2} = 2 \pi n + \operatorname{asin}{\left(w_{2} \right)}$$
$$x_{2} = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{5} \right)}$$
$$x_{2} = 2 \pi n - \operatorname{asin}{\left(\frac{1}{5} \right)}$$
$$x_{3} = 2 \pi n - \operatorname{asin}{\left(w_{1} \right)} + \pi$$
$$x_{3} = 2 \pi n - \operatorname{asin}{\left(\frac{1}{6} \right)} + \pi$$
$$x_{3} = 2 \pi n - \operatorname{asin}{\left(\frac{1}{6} \right)} + \pi$$
$$x_{4} = 2 \pi n - \operatorname{asin}{\left(w_{2} \right)} + \pi$$
$$x_{4} = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{5} \right)} + \pi$$
$$x_{4} = 2 \pi n + \operatorname{asin}{\left(\frac{1}{5} \right)} + \pi$$
Respuesta rápida
[src]
x1 = pi - asin(1/6)
$$x_{1} = \pi - \operatorname{asin}{\left(\frac{1}{6} \right)}$$
x2 = pi + asin(1/5)
$$x_{2} = \operatorname{asin}{\left(\frac{1}{5} \right)} + \pi$$
x3 = asin(1/6)
$$x_{3} = \operatorname{asin}{\left(\frac{1}{6} \right)}$$
x4 = -asin(1/5)
$$x_{4} = - \operatorname{asin}{\left(\frac{1}{5} \right)}$$
x4 = -asin(1/5)
Suma y producto de raíces
[src]
suma
pi - asin(1/6) + pi + asin(1/5) + asin(1/6) - asin(1/5)
$$- \operatorname{asin}{\left(\frac{1}{5} \right)} + \left(\operatorname{asin}{\left(\frac{1}{6} \right)} + \left(\left(\pi - \operatorname{asin}{\left(\frac{1}{6} \right)}\right) + \left(\operatorname{asin}{\left(\frac{1}{5} \right)} + \pi\right)\right)\right)$$
=
2*pi
$$2 \pi$$
producto
(pi - asin(1/6))*(pi + asin(1/5))*asin(1/6)*(-asin(1/5))
$$\left(\pi - \operatorname{asin}{\left(\frac{1}{6} \right)}\right) \left(\operatorname{asin}{\left(\frac{1}{5} \right)} + \pi\right) \operatorname{asin}{\left(\frac{1}{6} \right)} \left(- \operatorname{asin}{\left(\frac{1}{5} \right)}\right)$$
=
-(pi - asin(1/6))*(pi + asin(1/5))*asin(1/5)*asin(1/6)
$$- \left(\pi - \operatorname{asin}{\left(\frac{1}{6} \right)}\right) \left(\operatorname{asin}{\left(\frac{1}{5} \right)} + \pi\right) \operatorname{asin}{\left(\frac{1}{6} \right)} \operatorname{asin}{\left(\frac{1}{5} \right)}$$
-(pi - asin(1/6))*(pi + asin(1/5))*asin(1/5)*asin(1/6)
Respuesta numérica
[src]
x1 = -84.6216437261341
x2 = 66.174803646176
x3 = 97.5907301820739
x4 = 56.3473098438259
x5 = 59.8916183389964
x6 = 112.895977608442
x7 = -72.0552731117749
x8 = 91.3075448748943
x9 = 47.3252477246372
x10 = 62.6304951510055
x11 = 24.931383307928
x12 = 78.3723682605251
x13 = 22.1925064959189
x14 = -12.3989225351395
x15 = -9.59222603998907
x16 = -6.1157372279599
x17 = -62.6644049925762
x18 = 68.9136804581851
x19 = -34.3561612686974
x20 = 2.9741445743701
x21 = -65.7720878045953
x22 = -50.098034378217
x23 = 72.0891829533456
x24 = 100.329606994083
x25 = 15.9093211887393
x26 = -3.30904073280948
x27 = 44.1497452294768
x28 = 88.1320423797339
x29 = -40.639346575877
x30 = -97.1880143404933
x31 = 6.08182738638926
x32 = -43.8148490710374
x33 = 31.5833746151176
x34 = 9.62613588155971
x35 = 37297.1554314972
x36 = 46.9564417246272
x37 = -100.363516835654
x38 = -37.9004697638678
x39 = 25.300189307938
x40 = -41.008152575887
x41 = 12.3650126935688
x42 = -7326.39542609219
x43 = -75.5995816069454
x44 = -63.0332109925862
x45 = -28.0729759615178
x46 = 28.1068858030884
x47 = 3.34295057438012
x48 = -69.3163962997658
x49 = -25.3340991495087
x50 = -19.0509138423291
x51 = -97.5568203405033
x52 = -15.8754113471687
x53 = -87.7971462212945
x54 = 18.6481980007484
x55 = -91.2736350333237
x56 = 75.5656717653747
x57 = 53.6084330318168
x58 = 40.6732564174476
x59 = -147.82230279794
x60 = -18.6821078423191
x61 = -194.611296443347
x62 = 94.0464216869035
x63 = -21.7897906543382
x64 = 84.6555535677047
x65 = -47.2913378830666
x66 = 90.9387388748843
x67 = -78.3384584189545
x68 = 69.2824864581951
x69 = -31.6172844566883
x70 = 81.8488570725543
x71 = 50.0641245366464
x72 = -56.3812196853966
x73 = -84.9904497261441
x74 = 37.8665599222972
x75 = 0.167448079219689
x76 = 34.390071110268
x77 = -94.0803315284741
x78 = -81.882766914125
x79 = -53.5745231902462
x80 = -59.8577084974258
x80 = -59.8577084974258