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- La ecuación:
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Ecuación x/4+13=x+1
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Ecuación 0,2x+2,7=1,4-1,1x
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Ecuación 2x^2-x-1=x^2-5x-(-1-x^2)
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Ecuación 5(x-2)^2=-6x-44
- Expresar {x} en función de y en la ecuación:
- -2*x+14*y=9
- -6*x-20*y=8
- 2*x-8*y=4
- -9*x-1*y=6
-
Expresiones idénticas
- (x^ dos)*sin(y)- uno = cero
- (x al cuadrado ) multiplicar por seno de (y) menos 1 es igual a 0
- (x en el grado dos) multiplicar por seno de (y) menos uno es igual a cero
- (x2)*sin(y)-1=0
- x2*siny-1=0
- (x²)*sin(y)-1=0
- (x en el grado 2)*sin(y)-1=0
- (x^2)sin(y)-1=0
- (x2)sin(y)-1=0
- x2siny-1=0
- x^2siny-1=0
- (x^2)*sin(y)-1=O
-
Expresiones semejantes
- (x^2)*sin(y)+1=0
-
Expresiones con funciones
- Seno sin
- sin(x)=pi
- sin(x)=a
- sin(3*x)=-1
- sin(x)=1/3
- sin(4*x)=0
(x^2)*sin(y)-1=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Es la ecuación de la forma
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = \sin{\left(y \right)}$$
$$b = 0$$
$$c = -1$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = \frac{1}{\sqrt{\sin{\left(y \right)}}}$$
$$x_{2} = - \frac{1}{\sqrt{\sin{\left(y \right)}}}$$
a*x^2 + b*x + c = 0
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = \sin{\left(y \right)}$$
$$b = 0$$
$$c = -1$$
, entonces
D = b^2 - 4 * a * c =
(0)^2 - 4 * (sin(y)) * (-1) = 4*sin(y)
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = \frac{1}{\sqrt{\sin{\left(y \right)}}}$$
$$x_{2} = - \frac{1}{\sqrt{\sin{\left(y \right)}}}$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$x^{2} \sin{\left(y \right)} - 1 = 0$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$\frac{x^{2} \sin{\left(y \right)} - 1}{\sin{\left(y \right)}} = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - \frac{1}{\sin{\left(y \right)}}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = - \frac{1}{\sin{\left(y \right)}}$$
$$x^{2} \sin{\left(y \right)} - 1 = 0$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$\frac{x^{2} \sin{\left(y \right)} - 1}{\sin{\left(y \right)}} = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - \frac{1}{\sin{\left(y \right)}}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = - \frac{1}{\sin{\left(y \right)}}$$
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
$$x^{2} \sin{\left(y \right)} - 1 = 0$$
Коэффициент при x равен
$$\sin{\left(y \right)}$$
entonces son posibles los casos para y :
$$y < 0$$
$$y = 0$$
$$y > 0 \wedge y < \pi$$
$$y = \pi$$
Consideremos todos los casos con detalles:
Con
$$y < 0$$
la ecuación será
$$- x^{2} \sin{\left(1 \right)} - 1 = 0$$
su solución
no hay soluciones
Con
$$y = 0$$
la ecuación será
$$-1 = 0$$
su solución
no hay soluciones
Con
$$y > 0 \wedge y < \pi$$
la ecuación será
$$x^{2} - 1 = 0$$
su solución
$$x = -1$$
$$x = 1$$
Con
$$y = \pi$$
la ecuación será
$$-1 = 0$$
su solución
no hay soluciones
$$x^{2} \sin{\left(y \right)} - 1 = 0$$
Коэффициент при x равен
$$\sin{\left(y \right)}$$
entonces son posibles los casos para y :
$$y < 0$$
$$y = 0$$
$$y > 0 \wedge y < \pi$$
$$y = \pi$$
Consideremos todos los casos con detalles:
Con
$$y < 0$$
la ecuación será
$$- x^{2} \sin{\left(1 \right)} - 1 = 0$$
su solución
no hay soluciones
Con
$$y = 0$$
la ecuación será
$$-1 = 0$$
su solución
no hay soluciones
Con
$$y > 0 \wedge y < \pi$$
la ecuación será
$$x^{2} - 1 = 0$$
su solución
$$x = -1$$
$$x = 1$$
Con
$$y = \pi$$
la ecuación será
$$-1 = 0$$
su solución
no hay soluciones
Gráfica
Suma y producto de raíces
[src]
suma
/ / -cos(re(y))*sinh(im(y)) cosh(im(y))*sin(re(y)) \\ / / -cos(re(y))*sinh(im(y)) cosh(im(y))*sin(re(y)) \\ / / -cos(re(y))*sinh(im(y)) cosh(im(y))*sin(re(y)) \\ / / -cos(re(y))*sinh(im(y)) cosh(im(y))*sin(re(y)) \\
_________________________________________________________________________________________________________________ |atan2|---------------------------------------------------, ---------------------------------------------------|| _________________________________________________________________________________________________________________ |atan2|---------------------------------------------------, ---------------------------------------------------|| _________________________________________________________________________________________________________________ |atan2|---------------------------------------------------, ---------------------------------------------------|| _________________________________________________________________________________________________________________ |atan2|---------------------------------------------------, ---------------------------------------------------||
/ 2 2 2 2 | | 2 2 2 2 2 2 2 2 || / 2 2 2 2 | | 2 2 2 2 2 2 2 2 || / 2 2 2 2 | | 2 2 2 2 2 2 2 2 || / 2 2 2 2 | | 2 2 2 2 2 2 2 2 ||
/ cos (re(y))*sinh (im(y)) cosh (im(y))*sin (re(y)) | \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y)) cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/| / cos (re(y))*sinh (im(y)) cosh (im(y))*sin (re(y)) | \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y)) cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/| / cos (re(y))*sinh (im(y)) cosh (im(y))*sin (re(y)) | \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y)) cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/| / cos (re(y))*sinh (im(y)) cosh (im(y))*sin (re(y)) | \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y)) cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/|
- / ------------------------------------------------------ + ------------------------------------------------------ *cos|---------------------------------------------------------------------------------------------------------------| - I* / ------------------------------------------------------ + ------------------------------------------------------ *sin|---------------------------------------------------------------------------------------------------------------| + / ------------------------------------------------------ + ------------------------------------------------------ *cos|---------------------------------------------------------------------------------------------------------------| + I* / ------------------------------------------------------ + ------------------------------------------------------ *sin|---------------------------------------------------------------------------------------------------------------|
/ 2 2 \ 2 / / 2 2 \ 2 / / 2 2 \ 2 / / 2 2 \ 2 /
4 / / 2 2 2 2 \ / 2 2 2 2 \ 4 / / 2 2 2 2 \ / 2 2 2 2 \ 4 / / 2 2 2 2 \ / 2 2 2 2 \ 4 / / 2 2 2 2 \ / 2 2 2 2 \
\/ \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/ \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/ \/ \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/ \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/ \/ \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/ \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/ \/ \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/ \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/
$$\left(- i \sqrt[4]{\frac{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}}{\left(\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}\right)^{2}} + \frac{\cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}}{\left(\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}\right)^{2}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\cos{\left(\operatorname{re}{\left(y\right)} \right)} \sinh{\left(\operatorname{im}{\left(y\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}},\frac{\sin{\left(\operatorname{re}{\left(y\right)} \right)} \cosh{\left(\operatorname{im}{\left(y\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}} \right)}}{2} \right)} - \sqrt[4]{\frac{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}}{\left(\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}\right)^{2}} + \frac{\cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}}{\left(\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}\right)^{2}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\cos{\left(\operatorname{re}{\left(y\right)} \right)} \sinh{\left(\operatorname{im}{\left(y\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}},\frac{\sin{\left(\operatorname{re}{\left(y\right)} \right)} \cosh{\left(\operatorname{im}{\left(y\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}} \right)}}{2} \right)}\right) + \left(i \sqrt[4]{\frac{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}}{\left(\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}\right)^{2}} + \frac{\cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}}{\left(\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}\right)^{2}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\cos{\left(\operatorname{re}{\left(y\right)} \right)} \sinh{\left(\operatorname{im}{\left(y\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}},\frac{\sin{\left(\operatorname{re}{\left(y\right)} \right)} \cosh{\left(\operatorname{im}{\left(y\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}} \right)}}{2} \right)} + \sqrt[4]{\frac{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}}{\left(\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}\right)^{2}} + \frac{\cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}}{\left(\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}\right)^{2}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\cos{\left(\operatorname{re}{\left(y\right)} \right)} \sinh{\left(\operatorname{im}{\left(y\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}},\frac{\sin{\left(\operatorname{re}{\left(y\right)} \right)} \cosh{\left(\operatorname{im}{\left(y\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}} \right)}}{2} \right)}\right)$$
=
0
$$0$$
producto
/ / / -cos(re(y))*sinh(im(y)) cosh(im(y))*sin(re(y)) \\ / / -cos(re(y))*sinh(im(y)) cosh(im(y))*sin(re(y)) \\\ / / / -cos(re(y))*sinh(im(y)) cosh(im(y))*sin(re(y)) \\ / / -cos(re(y))*sinh(im(y)) cosh(im(y))*sin(re(y)) \\\ | _________________________________________________________________________________________________________________ |atan2|---------------------------------------------------, ---------------------------------------------------|| _________________________________________________________________________________________________________________ |atan2|---------------------------------------------------, ---------------------------------------------------||| | _________________________________________________________________________________________________________________ |atan2|---------------------------------------------------, ---------------------------------------------------|| _________________________________________________________________________________________________________________ |atan2|---------------------------------------------------, ---------------------------------------------------||| | / 2 2 2 2 | | 2 2 2 2 2 2 2 2 || / 2 2 2 2 | | 2 2 2 2 2 2 2 2 ||| | / 2 2 2 2 | | 2 2 2 2 2 2 2 2 || / 2 2 2 2 | | 2 2 2 2 2 2 2 2 ||| | / cos (re(y))*sinh (im(y)) cosh (im(y))*sin (re(y)) | \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y)) cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/| / cos (re(y))*sinh (im(y)) cosh (im(y))*sin (re(y)) | \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y)) cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/|| | / cos (re(y))*sinh (im(y)) cosh (im(y))*sin (re(y)) | \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y)) cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/| / cos (re(y))*sinh (im(y)) cosh (im(y))*sin (re(y)) | \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y)) cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/|| |- / ------------------------------------------------------ + ------------------------------------------------------ *cos|---------------------------------------------------------------------------------------------------------------| - I* / ------------------------------------------------------ + ------------------------------------------------------ *sin|---------------------------------------------------------------------------------------------------------------||*| / ------------------------------------------------------ + ------------------------------------------------------ *cos|---------------------------------------------------------------------------------------------------------------| + I* / ------------------------------------------------------ + ------------------------------------------------------ *sin|---------------------------------------------------------------------------------------------------------------|| | / 2 2 \ 2 / / 2 2 \ 2 /| | / 2 2 \ 2 / / 2 2 \ 2 /| | 4 / / 2 2 2 2 \ / 2 2 2 2 \ 4 / / 2 2 2 2 \ / 2 2 2 2 \ | |4 / / 2 2 2 2 \ / 2 2 2 2 \ 4 / / 2 2 2 2 \ / 2 2 2 2 \ | \ \/ \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/ \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/ \/ \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/ \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/ / \\/ \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/ \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/ \/ \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/ \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/ /
$$\left(- i \sqrt[4]{\frac{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}}{\left(\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}\right)^{2}} + \frac{\cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}}{\left(\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}\right)^{2}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\cos{\left(\operatorname{re}{\left(y\right)} \right)} \sinh{\left(\operatorname{im}{\left(y\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}},\frac{\sin{\left(\operatorname{re}{\left(y\right)} \right)} \cosh{\left(\operatorname{im}{\left(y\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}} \right)}}{2} \right)} - \sqrt[4]{\frac{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}}{\left(\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}\right)^{2}} + \frac{\cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}}{\left(\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}\right)^{2}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\cos{\left(\operatorname{re}{\left(y\right)} \right)} \sinh{\left(\operatorname{im}{\left(y\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}},\frac{\sin{\left(\operatorname{re}{\left(y\right)} \right)} \cosh{\left(\operatorname{im}{\left(y\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}} \right)}}{2} \right)}\right) \left(i \sqrt[4]{\frac{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}}{\left(\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}\right)^{2}} + \frac{\cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}}{\left(\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}\right)^{2}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\cos{\left(\operatorname{re}{\left(y\right)} \right)} \sinh{\left(\operatorname{im}{\left(y\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}},\frac{\sin{\left(\operatorname{re}{\left(y\right)} \right)} \cosh{\left(\operatorname{im}{\left(y\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}} \right)}}{2} \right)} + \sqrt[4]{\frac{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}}{\left(\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}\right)^{2}} + \frac{\cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}}{\left(\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}\right)^{2}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\cos{\left(\operatorname{re}{\left(y\right)} \right)} \sinh{\left(\operatorname{im}{\left(y\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}},\frac{\sin{\left(\operatorname{re}{\left(y\right)} \right)} \cosh{\left(\operatorname{im}{\left(y\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}} \right)}}{2} \right)}\right)$$
=
2
/ / / -cos(re(y))*sinh(im(y)) cosh(im(y))*sin(re(y)) \\ / / -cos(re(y))*sinh(im(y)) cosh(im(y))*sin(re(y)) \\\
| |atan2|---------------------------------------------------, ---------------------------------------------------|| |atan2|---------------------------------------------------, ---------------------------------------------------|||
| | | 2 2 2 2 2 2 2 2 || | | 2 2 2 2 2 2 2 2 |||
| | \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y)) cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/| | \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y)) cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/||
-|I*sin|---------------------------------------------------------------------------------------------------------------| + cos|---------------------------------------------------------------------------------------------------------------||
\ \ 2 / \ 2 //
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
_____________________________________________________
/ 2 2 2 2
\/ cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))
$$- \frac{\left(i \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\cos{\left(\operatorname{re}{\left(y\right)} \right)} \sinh{\left(\operatorname{im}{\left(y\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}},\frac{\sin{\left(\operatorname{re}{\left(y\right)} \right)} \cosh{\left(\operatorname{im}{\left(y\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}} \right)}}{2} \right)} + \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\cos{\left(\operatorname{re}{\left(y\right)} \right)} \sinh{\left(\operatorname{im}{\left(y\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}},\frac{\sin{\left(\operatorname{re}{\left(y\right)} \right)} \cosh{\left(\operatorname{im}{\left(y\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}} \right)}}{2} \right)}\right)^{2}}{\sqrt{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}}}$$
-(i*sin(atan2(-cos(re(y))*sinh(im(y))/(cos(re(y))^2*sinh(im(y))^2 + cosh(im(y))^2*sin(re(y))^2), cosh(im(y))*sin(re(y))/(cos(re(y))^2*sinh(im(y))^2 + cosh(im(y))^2*sin(re(y))^2))/2) + cos(atan2(-cos(re(y))*sinh(im(y))/(cos(re(y))^2*sinh(im(y))^2 + cosh(im(y))^2*sin(re(y))^2), cosh(im(y))*sin(re(y))/(cos(re(y))^2*sinh(im(y))^2 + cosh(im(y))^2*sin(re(y))^2))/2))^2/sqrt(cos(re(y))^2*sinh(im(y))^2 + cosh(im(y))^2*sin(re(y))^2)
Respuesta rápida
[src]
/ / -cos(re(y))*sinh(im(y)) cosh(im(y))*sin(re(y)) \\ / / -cos(re(y))*sinh(im(y)) cosh(im(y))*sin(re(y)) \\
_________________________________________________________________________________________________________________ |atan2|---------------------------------------------------, ---------------------------------------------------|| _________________________________________________________________________________________________________________ |atan2|---------------------------------------------------, ---------------------------------------------------||
/ 2 2 2 2 | | 2 2 2 2 2 2 2 2 || / 2 2 2 2 | | 2 2 2 2 2 2 2 2 ||
/ cos (re(y))*sinh (im(y)) cosh (im(y))*sin (re(y)) | \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y)) cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/| / cos (re(y))*sinh (im(y)) cosh (im(y))*sin (re(y)) | \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y)) cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/|
x1 = - / ------------------------------------------------------ + ------------------------------------------------------ *cos|---------------------------------------------------------------------------------------------------------------| - I* / ------------------------------------------------------ + ------------------------------------------------------ *sin|---------------------------------------------------------------------------------------------------------------|
/ 2 2 \ 2 / / 2 2 \ 2 /
4 / / 2 2 2 2 \ / 2 2 2 2 \ 4 / / 2 2 2 2 \ / 2 2 2 2 \
\/ \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/ \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/ \/ \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/ \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/
$$x_{1} = - i \sqrt[4]{\frac{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}}{\left(\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}\right)^{2}} + \frac{\cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}}{\left(\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}\right)^{2}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\cos{\left(\operatorname{re}{\left(y\right)} \right)} \sinh{\left(\operatorname{im}{\left(y\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}},\frac{\sin{\left(\operatorname{re}{\left(y\right)} \right)} \cosh{\left(\operatorname{im}{\left(y\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}} \right)}}{2} \right)} - \sqrt[4]{\frac{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}}{\left(\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}\right)^{2}} + \frac{\cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}}{\left(\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}\right)^{2}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\cos{\left(\operatorname{re}{\left(y\right)} \right)} \sinh{\left(\operatorname{im}{\left(y\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}},\frac{\sin{\left(\operatorname{re}{\left(y\right)} \right)} \cosh{\left(\operatorname{im}{\left(y\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}} \right)}}{2} \right)}$$
/ / -cos(re(y))*sinh(im(y)) cosh(im(y))*sin(re(y)) \\ / / -cos(re(y))*sinh(im(y)) cosh(im(y))*sin(re(y)) \\
_________________________________________________________________________________________________________________ |atan2|---------------------------------------------------, ---------------------------------------------------|| _________________________________________________________________________________________________________________ |atan2|---------------------------------------------------, ---------------------------------------------------||
/ 2 2 2 2 | | 2 2 2 2 2 2 2 2 || / 2 2 2 2 | | 2 2 2 2 2 2 2 2 ||
/ cos (re(y))*sinh (im(y)) cosh (im(y))*sin (re(y)) | \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y)) cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/| / cos (re(y))*sinh (im(y)) cosh (im(y))*sin (re(y)) | \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y)) cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/|
x2 = / ------------------------------------------------------ + ------------------------------------------------------ *cos|---------------------------------------------------------------------------------------------------------------| + I* / ------------------------------------------------------ + ------------------------------------------------------ *sin|---------------------------------------------------------------------------------------------------------------|
/ 2 2 \ 2 / / 2 2 \ 2 /
4 / / 2 2 2 2 \ / 2 2 2 2 \ 4 / / 2 2 2 2 \ / 2 2 2 2 \
\/ \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/ \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/ \/ \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/ \cos (re(y))*sinh (im(y)) + cosh (im(y))*sin (re(y))/
$$x_{2} = i \sqrt[4]{\frac{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}}{\left(\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}\right)^{2}} + \frac{\cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}}{\left(\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}\right)^{2}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\cos{\left(\operatorname{re}{\left(y\right)} \right)} \sinh{\left(\operatorname{im}{\left(y\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}},\frac{\sin{\left(\operatorname{re}{\left(y\right)} \right)} \cosh{\left(\operatorname{im}{\left(y\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}} \right)}}{2} \right)} + \sqrt[4]{\frac{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}}{\left(\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}\right)^{2}} + \frac{\cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}}{\left(\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}\right)^{2}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\cos{\left(\operatorname{re}{\left(y\right)} \right)} \sinh{\left(\operatorname{im}{\left(y\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}},\frac{\sin{\left(\operatorname{re}{\left(y\right)} \right)} \cosh{\left(\operatorname{im}{\left(y\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(y\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(y\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(y\right)} \right)}} \right)}}{2} \right)}$$
x2 = i*(sin(re(y))^2*cosh(im(y))^2/(sin(re(y))^2*cosh(im(y))^2 + cos(re(y))^2*sinh(im(y))^2)^2 + cos(re(y))^2*sinh(im(y))^2/(sin(re(y))^2*cosh(im(y))^2 + cos(re(y))^2*sinh(im(y))^2)^2)^(1/4)*sin(atan2(-cos(re(y))*sinh(im(y))/(sin(re(y))^2*cosh(im(y))^2 + cos(re(y))^2*sinh(im(y))^2, sin(re(y))*cosh(im(y))/(sin(re(y))^2*cosh(im(y))^2 + cos(re(y))^2*sinh(im(y))^2))/2) + (sin(re(y))^2*cosh(im(y))^2/(sin(re(y))^2*cosh(im(y))^2 + cos(re(y))^2*sinh(im(y))^2)^2 + cos(re(y))^2*sinh(im(y))^2/(sin(re(y))^2*cosh(im(y))^2 + cos(re(y))^2*sinh(im(y))^2)^2)^(1/4)*cos(atan2(-cos(re(y))*sinh(im(y))/(sin(re(y))^2*cosh(im(y))^2 + cos(re(y))^2*sinh(im(y))^2), sin(re(y))*cosh(im(y))/(sin(re(y))^2*cosh(im(y))^2 + cos(re(y))^2*sinh(im(y))^2))/2))