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- La ecuación:
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Ecuación x+9=0
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Ecuación 2x^2+7x-9=0
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Ecuación 3,4+2y=7(y-2,3)
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Ecuación 9x-4x+39=94
- Expresar {x} en función de y en la ecuación:
- -16*x+3*y=17
- 18*x-14*y=-2
- 18*x+19*y=10
- 11*x-6*y=5
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Expresiones idénticas
- sin(dos *y)^ dos =x
- seno de (2 multiplicar por y) al cuadrado es igual a x
- seno de (dos multiplicar por y) en el grado dos es igual a x
- sin(2*y)2=x
- sin2*y2=x
- sin(2*y)²=x
- sin(2*y) en el grado 2=x
- sin(2y)^2=x
- sin(2y)2=x
- sin2y2=x
- sin2y^2=x
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Expresiones con funciones
- Seno sin
- sin(x/4)*sin(x/4)-cos(x/4)*cos(x/4)=cos(x)
- sin(3x/2+П/3)+1=0
- sin+1=0
- sin(3*x)-3=0
- sin(4*x+pi/2)=0
sin(2*y)^2=x la ecuación
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Solución
Solución detallada
Tenemos la ecuación
$$\sin^{2}{\left(2 y \right)} = x$$
cambiamos
$$- x + \sin^{2}{\left(2 y \right)} - 1 = 0$$
$$- x + \sin^{2}{\left(2 y \right)} - 1 = 0$$
Sustituimos
$$w = \sin{\left(2 y \right)}$$
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
$$a = 1$$
$$b = 0$$
$$c = - x - 1$$
, entonces
La ecuación tiene dos raíces.
o
$$w_{1} = \frac{\sqrt{4 x + 4}}{2}$$
$$w_{2} = - \frac{\sqrt{4 x + 4}}{2}$$
hacemos cambio inverso
$$\sin{\left(2 y \right)} = w$$
sustituimos w:
$$\sin^{2}{\left(2 y \right)} = x$$
cambiamos
$$- x + \sin^{2}{\left(2 y \right)} - 1 = 0$$
$$- x + \sin^{2}{\left(2 y \right)} - 1 = 0$$
Sustituimos
$$w = \sin{\left(2 y \right)}$$
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
$$a = 1$$
$$b = 0$$
$$c = - x - 1$$
, entonces
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (-1 - x) = 4 + 4*x
La ecuación tiene dos raíces.
w1 = (-b + sqrt(D)) / (2*a)
w2 = (-b - sqrt(D)) / (2*a)
o
$$w_{1} = \frac{\sqrt{4 x + 4}}{2}$$
$$w_{2} = - \frac{\sqrt{4 x + 4}}{2}$$
hacemos cambio inverso
$$\sin{\left(2 y \right)} = w$$
sustituimos w:
Gráfica
Respuesta rápida
[src]
2 2 2 2 x1 = cosh (2*im(y))*sin (2*re(y)) - cos (2*re(y))*sinh (2*im(y)) + 2*I*cos(2*re(y))*cosh(2*im(y))*sin(2*re(y))*sinh(2*im(y))
$$x_{1} = \sin^{2}{\left(2 \operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(2 \operatorname{im}{\left(y\right)} \right)} + 2 i \sin{\left(2 \operatorname{re}{\left(y\right)} \right)} \cos{\left(2 \operatorname{re}{\left(y\right)} \right)} \sinh{\left(2 \operatorname{im}{\left(y\right)} \right)} \cosh{\left(2 \operatorname{im}{\left(y\right)} \right)} - \cos^{2}{\left(2 \operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(2 \operatorname{im}{\left(y\right)} \right)}$$
x1 = sin(2*re(y))^2*cosh(2*im(y))^2 + 2*i*sin(2*re(y))*cos(2*re(y))*sinh(2*im(y))*cosh(2*im(y)) - cos(2*re(y))^2*sinh(2*im(y))^2
Suma y producto de raíces
[src]
suma
2 2 2 2 cosh (2*im(y))*sin (2*re(y)) - cos (2*re(y))*sinh (2*im(y)) + 2*I*cos(2*re(y))*cosh(2*im(y))*sin(2*re(y))*sinh(2*im(y))
$$\sin^{2}{\left(2 \operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(2 \operatorname{im}{\left(y\right)} \right)} + 2 i \sin{\left(2 \operatorname{re}{\left(y\right)} \right)} \cos{\left(2 \operatorname{re}{\left(y\right)} \right)} \sinh{\left(2 \operatorname{im}{\left(y\right)} \right)} \cosh{\left(2 \operatorname{im}{\left(y\right)} \right)} - \cos^{2}{\left(2 \operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(2 \operatorname{im}{\left(y\right)} \right)}$$
=
2 2 2 2 cosh (2*im(y))*sin (2*re(y)) - cos (2*re(y))*sinh (2*im(y)) + 2*I*cos(2*re(y))*cosh(2*im(y))*sin(2*re(y))*sinh(2*im(y))
$$\sin^{2}{\left(2 \operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(2 \operatorname{im}{\left(y\right)} \right)} + 2 i \sin{\left(2 \operatorname{re}{\left(y\right)} \right)} \cos{\left(2 \operatorname{re}{\left(y\right)} \right)} \sinh{\left(2 \operatorname{im}{\left(y\right)} \right)} \cosh{\left(2 \operatorname{im}{\left(y\right)} \right)} - \cos^{2}{\left(2 \operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(2 \operatorname{im}{\left(y\right)} \right)}$$
producto
2 2 2 2 cosh (2*im(y))*sin (2*re(y)) - cos (2*re(y))*sinh (2*im(y)) + 2*I*cos(2*re(y))*cosh(2*im(y))*sin(2*re(y))*sinh(2*im(y))
$$\sin^{2}{\left(2 \operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(2 \operatorname{im}{\left(y\right)} \right)} + 2 i \sin{\left(2 \operatorname{re}{\left(y\right)} \right)} \cos{\left(2 \operatorname{re}{\left(y\right)} \right)} \sinh{\left(2 \operatorname{im}{\left(y\right)} \right)} \cosh{\left(2 \operatorname{im}{\left(y\right)} \right)} - \cos^{2}{\left(2 \operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(2 \operatorname{im}{\left(y\right)} \right)}$$
=
2 2 2 2 cosh (2*im(y))*sin (2*re(y)) - cos (2*re(y))*sinh (2*im(y)) + I*cosh(2*im(y))*sin(4*re(y))*sinh(2*im(y))
$$\sin^{2}{\left(2 \operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(2 \operatorname{im}{\left(y\right)} \right)} + i \sin{\left(4 \operatorname{re}{\left(y\right)} \right)} \sinh{\left(2 \operatorname{im}{\left(y\right)} \right)} \cosh{\left(2 \operatorname{im}{\left(y\right)} \right)} - \cos^{2}{\left(2 \operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(2 \operatorname{im}{\left(y\right)} \right)}$$
cosh(2*im(y))^2*sin(2*re(y))^2 - cos(2*re(y))^2*sinh(2*im(y))^2 + i*cosh(2*im(y))*sin(4*re(y))*sinh(2*im(y))