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- La ecuación:
-
Ecuación 3x-2=0
-
Ecuación x^2+7x=18
-
Ecuación 12-4(x-3)=39-9x
-
Ecuación 0,2x+2,7=1,4-1,1x
- Expresar {x} en función de y en la ecuación:
- -17*x+1*y=-11
- -8*x-15*y=15
- -3*x+17*y=-4
- -14*x-12*y=5
- Derivada de:
-
atan(y)
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sqrt(4-x^2)
- Integral de d{x}:
- sqrt(4-x^2)
- Gráfico de la función y =:
-
sqrt(4-x^2)
-
Expresiones idénticas
- atan(y)=sqrt(cuatro -x^ dos)
- arco tangente de gente de (y) es igual a raíz cuadrada de (4 menos x al cuadrado )
- arco tangente de gente de (y) es igual a raíz cuadrada de (cuatro menos x en el grado dos)
- atan(y)=√(4-x^2)
- atan(y)=sqrt(4-x2)
- atany=sqrt4-x2
- atan(y)=sqrt(4-x²)
- atan(y)=sqrt(4-x en el grado 2)
- atany=sqrt4-x^2
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Expresiones semejantes
- x.diff(x)*y-y=x/(atan(y/x))
- atan(y)=sqrt(4+x^2)
- -atan(y/2)/2=Const-atan(x/4)/4
- atan(y/3)/3=Const+x^2/2
- arctan(y)=sqrt(4-x^2)
-
Expresiones con funciones
- Arcotangente arctan
- atan(1/x)=o*(1)
- atan(x)-x^2+1=0
- atan(x)-(1/x^3)=0
- atan(x)=(2*(-1)^(m*m)*x^2+(-1)^((m*x)^2)+m^2+5*m-x^2+4)/4
- atan(x)+3*x=pi/2
- Raíz cuadrada sqrt
- sqrt(12+x)-sqrt(1-x)=1
- sqrt(x-1)+3=x
- sqrt(x^2-4)=4-2x
- sqrt(x-1)=x-3
- sqrt(x^2-x-3)=3
atan(y)=sqrt(4-x^2) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
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/ 2
atan(y) = \/ 4 - x
$$\operatorname{atan}{\left(y \right)} = \sqrt{4 - x^{2}}$$
Solución detallada
Tenemos la ecuación
$$\operatorname{atan}{\left(y \right)} = \sqrt{4 - x^{2}}$$
Transpongamos la parte derecha de la ecuación miembro izquierdo de la ecuación con el signo negativo
$$- \sqrt{4 - x^{2}} = - \operatorname{atan}{\left(y \right)}$$
Elevemos las dos partes de la ecuación a la potencia 2
$$4 - x^{2} = \operatorname{atan}^{2}{\left(y \right)}$$
$$4 - x^{2} = \operatorname{atan}^{2}{\left(y \right)}$$
Transpongamos la parte derecha de la ecuación miembro izquierdo de la ecuación con el signo negativo
$$- x^{2} - \operatorname{atan}^{2}{\left(y \right)} + 4 = 0$$
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
$$a = -1$$
$$b = 0$$
$$c = 4 - \operatorname{atan}^{2}{\left(y \right)}$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = - \frac{\sqrt{16 - 4 \operatorname{atan}^{2}{\left(y \right)}}}{2}$$
$$x_{2} = \frac{\sqrt{16 - 4 \operatorname{atan}^{2}{\left(y \right)}}}{2}$$
$$\operatorname{atan}{\left(y \right)} = \sqrt{4 - x^{2}}$$
Transpongamos la parte derecha de la ecuación miembro izquierdo de la ecuación con el signo negativo
$$- \sqrt{4 - x^{2}} = - \operatorname{atan}{\left(y \right)}$$
Elevemos las dos partes de la ecuación a la potencia 2
$$4 - x^{2} = \operatorname{atan}^{2}{\left(y \right)}$$
$$4 - x^{2} = \operatorname{atan}^{2}{\left(y \right)}$$
Transpongamos la parte derecha de la ecuación miembro izquierdo de la ecuación con el signo negativo
$$- x^{2} - \operatorname{atan}^{2}{\left(y \right)} + 4 = 0$$
Es la ecuación de la forma
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
$$a = -1$$
$$b = 0$$
$$c = 4 - \operatorname{atan}^{2}{\left(y \right)}$$
, entonces
D = b^2 - 4 * a * c =
(0)^2 - 4 * (-1) * (4 - atan(y)^2) = 16 - 4*atan(y)^2
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = - \frac{\sqrt{16 - 4 \operatorname{atan}^{2}{\left(y \right)}}}{2}$$
$$x_{2} = \frac{\sqrt{16 - 4 \operatorname{atan}^{2}{\left(y \right)}}}{2}$$
Gráfica
Suma y producto de raíces
[src]
suma
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/ 2 / / 2 2 \\ / 2 / / 2 2 \\ / 2 / / 2 2 \\ / 2 / / 2 2 \\
4 / / 2 2 \ 2 2 |atan2\-2*im(atan(y))*re(atan(y)), 4 + im (atan(y)) - re (atan(y))/| 4 / / 2 2 \ 2 2 |atan2\-2*im(atan(y))*re(atan(y)), 4 + im (atan(y)) - re (atan(y))/| 4 / / 2 2 \ 2 2 |atan2\-2*im(atan(y))*re(atan(y)), 4 + im (atan(y)) - re (atan(y))/| 4 / / 2 2 \ 2 2 |atan2\-2*im(atan(y))*re(atan(y)), 4 + im (atan(y)) - re (atan(y))/|
- \/ \4 + im (atan(y)) - re (atan(y))/ + 4*im (atan(y))*re (atan(y)) *cos|------------------------------------------------------------------| - I*\/ \4 + im (atan(y)) - re (atan(y))/ + 4*im (atan(y))*re (atan(y)) *sin|------------------------------------------------------------------| + \/ \4 + im (atan(y)) - re (atan(y))/ + 4*im (atan(y))*re (atan(y)) *cos|------------------------------------------------------------------| + I*\/ \4 + im (atan(y)) - re (atan(y))/ + 4*im (atan(y))*re (atan(y)) *sin|------------------------------------------------------------------|
\ 2 / \ 2 / \ 2 / \ 2 /
$$\left(- i \sqrt[4]{\left(- \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + 4\right)^{2} + 4 \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)} \operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)},- \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + 4 \right)}}{2} \right)} - \sqrt[4]{\left(- \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + 4\right)^{2} + 4 \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)} \operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)},- \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + 4 \right)}}{2} \right)}\right) + \left(i \sqrt[4]{\left(- \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + 4\right)^{2} + 4 \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)} \operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)},- \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + 4 \right)}}{2} \right)} + \sqrt[4]{\left(- \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + 4\right)^{2} + 4 \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)} \operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)},- \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + 4 \right)}}{2} \right)}\right)$$
=
0
$$0$$
producto
/ __________________________________________________________________ __________________________________________________________________ \ / __________________________________________________________________ __________________________________________________________________ \ | / 2 / / 2 2 \\ / 2 / / 2 2 \\| | / 2 / / 2 2 \\ / 2 / / 2 2 \\| | 4 / / 2 2 \ 2 2 |atan2\-2*im(atan(y))*re(atan(y)), 4 + im (atan(y)) - re (atan(y))/| 4 / / 2 2 \ 2 2 |atan2\-2*im(atan(y))*re(atan(y)), 4 + im (atan(y)) - re (atan(y))/|| |4 / / 2 2 \ 2 2 |atan2\-2*im(atan(y))*re(atan(y)), 4 + im (atan(y)) - re (atan(y))/| 4 / / 2 2 \ 2 2 |atan2\-2*im(atan(y))*re(atan(y)), 4 + im (atan(y)) - re (atan(y))/|| |- \/ \4 + im (atan(y)) - re (atan(y))/ + 4*im (atan(y))*re (atan(y)) *cos|------------------------------------------------------------------| - I*\/ \4 + im (atan(y)) - re (atan(y))/ + 4*im (atan(y))*re (atan(y)) *sin|------------------------------------------------------------------||*|\/ \4 + im (atan(y)) - re (atan(y))/ + 4*im (atan(y))*re (atan(y)) *cos|------------------------------------------------------------------| + I*\/ \4 + im (atan(y)) - re (atan(y))/ + 4*im (atan(y))*re (atan(y)) *sin|------------------------------------------------------------------|| \ \ 2 / \ 2 // \ \ 2 / \ 2 //
$$\left(- i \sqrt[4]{\left(- \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + 4\right)^{2} + 4 \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)} \operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)},- \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + 4 \right)}}{2} \right)} - \sqrt[4]{\left(- \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + 4\right)^{2} + 4 \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)} \operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)},- \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + 4 \right)}}{2} \right)}\right) \left(i \sqrt[4]{\left(- \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + 4\right)^{2} + 4 \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)} \operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)},- \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + 4 \right)}}{2} \right)} + \sqrt[4]{\left(- \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + 4\right)^{2} + 4 \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)} \operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)},- \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + 4 \right)}}{2} \right)}\right)$$
=
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/ 2 / 2 2 \
/ / 2 2 \ 2 2 I*atan2\-2*im(atan(y))*re(atan(y)), 4 + im (atan(y)) - re (atan(y))/
-\/ \4 + im (atan(y)) - re (atan(y))/ + 4*im (atan(y))*re (atan(y)) *e
$$- \sqrt{\left(- \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + 4\right)^{2} + 4 \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2}} e^{i \operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)} \operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)},- \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + 4 \right)}}$$
-sqrt((4 + im(atan(y))^2 - re(atan(y))^2)^2 + 4*im(atan(y))^2*re(atan(y))^2)*exp(i*atan2(-2*im(atan(y))*re(atan(y)), 4 + im(atan(y))^2 - re(atan(y))^2))
Respuesta rápida
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/ 2 / / 2 2 \\ / 2 / / 2 2 \\
4 / / 2 2 \ 2 2 |atan2\-2*im(atan(y))*re(atan(y)), 4 + im (atan(y)) - re (atan(y))/| 4 / / 2 2 \ 2 2 |atan2\-2*im(atan(y))*re(atan(y)), 4 + im (atan(y)) - re (atan(y))/|
x1 = - \/ \4 + im (atan(y)) - re (atan(y))/ + 4*im (atan(y))*re (atan(y)) *cos|------------------------------------------------------------------| - I*\/ \4 + im (atan(y)) - re (atan(y))/ + 4*im (atan(y))*re (atan(y)) *sin|------------------------------------------------------------------|
\ 2 / \ 2 /
$$x_{1} = - i \sqrt[4]{\left(- \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + 4\right)^{2} + 4 \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)} \operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)},- \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + 4 \right)}}{2} \right)} - \sqrt[4]{\left(- \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + 4\right)^{2} + 4 \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)} \operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)},- \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + 4 \right)}}{2} \right)}$$
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/ 2 / / 2 2 \\ / 2 / / 2 2 \\
4 / / 2 2 \ 2 2 |atan2\-2*im(atan(y))*re(atan(y)), 4 + im (atan(y)) - re (atan(y))/| 4 / / 2 2 \ 2 2 |atan2\-2*im(atan(y))*re(atan(y)), 4 + im (atan(y)) - re (atan(y))/|
x2 = \/ \4 + im (atan(y)) - re (atan(y))/ + 4*im (atan(y))*re (atan(y)) *cos|------------------------------------------------------------------| + I*\/ \4 + im (atan(y)) - re (atan(y))/ + 4*im (atan(y))*re (atan(y)) *sin|------------------------------------------------------------------|
\ 2 / \ 2 /
$$x_{2} = i \sqrt[4]{\left(- \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + 4\right)^{2} + 4 \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)} \operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)},- \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + 4 \right)}}{2} \right)} + \sqrt[4]{\left(- \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + 4\right)^{2} + 4 \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)} \operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)},- \left(\operatorname{re}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + \left(\operatorname{im}{\left(\operatorname{atan}{\left(y \right)}\right)}\right)^{2} + 4 \right)}}{2} \right)}$$
x2 = i*((-re(atan(y))^2 + im(atan(y))^2 + 4)^2 + 4*re(atan(y))^2*im(atan(y))^2)^(1/4)*sin(atan2(-2*re(atan(y))*im(atan(y), -re(atan(y))^2 + im(atan(y))^2 + 4)/2) + ((-re(atan(y))^2 + im(atan(y))^2 + 4)^2 + 4*re(atan(y))^2*im(atan(y))^2)^(1/4)*cos(atan2(-2*re(atan(y))*im(atan(y)), -re(atan(y))^2 + im(atan(y))^2 + 4)/2))