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- La ecuación:
-
Ecuación x+9=0
-
Ecuación 3,4+2y=7(y-2,3)
- Ecuación z^3=1+i
-
Ecuación x/(x-2)-7/(x+2)=8/(x^2-4)
- 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
- Integral de d{x}:
- sin^2(x)*cos^2(x)
- Derivada de:
-
-1
- Límite de la función:
-
-1
- Forma canónica:
- -1
-
Expresiones idénticas
- sin^ dos (x)*cos^ dos (x)=- uno
- seno de al cuadrado (x) multiplicar por coseno de al cuadrado (x) es igual a menos 1
- seno de en el grado dos (x) multiplicar por coseno de en el grado dos (x) es igual a menos uno
- sin2(x)*cos2(x)=-1
- sin2x*cos2x=-1
- sin²(x)*cos²(x)=-1
- sin en el grado 2(x)*cos en el grado 2(x)=-1
- sin^2(x)cos^2(x)=-1
- sin2(x)cos2(x)=-1
- sin2xcos2x=-1
- sin^2xcos^2x=-1
-
Expresiones semejantes
- sin^2(x)*cos^2(x)=+1
-
Expresiones con funciones
- Seno sin
- sin(x/4)*sin(x/4)-cos(x/4)*cos(x/4)=cos(x)
- sin(2*y)^2=x
- sin(4*x+pi/2)=0
- sin(x)=(1/2)*x+1
- sin^2(x/2)+sin^2(x)+sin^2(5x\2)+sin^2(x)=2
- Coseno cos
- cos(3*x)-cos(7x)=0
- cos^2(2*pi*50*t)=0,995
- cos2a2,cosa=1447.
- cos5a-cos3a
- cos(п/2)=-1
sin^2(x)*cos^2(x)=-1 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 2 sin (x)*cos (x) = -1
$$\sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)} = -1$$
Solución detallada
Tenemos la ecuación
$$\sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)} = -1$$
cambiamos
$$\frac{1}{8} - \frac{\cos{\left(4 x \right)}}{8} = 0$$
$$\sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)} = 0$$
Sustituimos
$$w = \cos{\left(x \right)}$$
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
$$a = \sin^{2}{\left(x \right)}$$
$$b = 0$$
$$c = 0$$
, entonces
Como D = 0 hay sólo una raíz.
$$w_{1} = 0$$
hacemos cambio inverso
$$\cos{\left(x \right)} = w$$
Tenemos la ecuación
$$\cos{\left(x \right)} = w$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = \pi n + \operatorname{acos}{\left(w \right)}$$
$$x = \pi n + \operatorname{acos}{\left(w \right)} - \pi$$
O
$$x = \pi n + \operatorname{acos}{\left(w \right)}$$
$$x = \pi n + \operatorname{acos}{\left(w \right)} - \pi$$
, donde n es cualquier número entero
sustituimos w:
$$x_{1} = \pi n + \operatorname{acos}{\left(w_{1} \right)}$$
$$x_{1} = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$x_{1} = \pi n + \frac{\pi}{2}$$
$$x_{2} = \pi n + \operatorname{acos}{\left(w_{1} \right)} - \pi$$
$$x_{2} = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
$$x_{2} = \pi n - \frac{\pi}{2}$$
$$\sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)} = -1$$
cambiamos
$$\frac{1}{8} - \frac{\cos{\left(4 x \right)}}{8} = 0$$
$$\sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)} = 0$$
Sustituimos
$$w = \cos{\left(x \right)}$$
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
$$a = \sin^{2}{\left(x \right)}$$
$$b = 0$$
$$c = 0$$
, entonces
D = b^2 - 4 * a * c =
(0)^2 - 4 * (sin(x)^2) * (0) = 0
Como D = 0 hay sólo una raíz.
w = -b/2a = -0/2/(sin(x)^2)
$$w_{1} = 0$$
hacemos cambio inverso
$$\cos{\left(x \right)} = w$$
Tenemos la ecuación
$$\cos{\left(x \right)} = w$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = \pi n + \operatorname{acos}{\left(w \right)}$$
$$x = \pi n + \operatorname{acos}{\left(w \right)} - \pi$$
O
$$x = \pi n + \operatorname{acos}{\left(w \right)}$$
$$x = \pi n + \operatorname{acos}{\left(w \right)} - \pi$$
, donde n es cualquier número entero
sustituimos w:
$$x_{1} = \pi n + \operatorname{acos}{\left(w_{1} \right)}$$
$$x_{1} = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$x_{1} = \pi n + \frac{\pi}{2}$$
$$x_{2} = \pi n + \operatorname{acos}{\left(w_{1} \right)} - \pi$$
$$x_{2} = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
$$x_{2} = \pi n - \frac{\pi}{2}$$
Suma y producto de raíces
[src]
suma
/ / / 2 \ \\ / / / 2 \ \\ / / / 2 \ \\ / / / 2 \ \\ / / / 2 \\\ / / / 2 \\\ / / / 2 \\\ / / / 2 \\\
| | -I*atan|---------------| || | | -I*atan|---------------| || | | -I*atan|---------------| || | | -I*atan|---------------| || | | I*atan|---------------||| | | I*atan|---------------||| | | I*atan|---------------||| | | I*atan|---------------|||
| | | ____________| || | | | ____________| || | | | ____________| || | | | ____________| || | | | ____________||| | | | ____________||| | | | ____________||| | | | ____________|||
| | | / ___ | || | | | / ___ | || | | | / ___ | || | | | / ___ | || | | | / ___ ||| | | | / ___ ||| | | | / ___ ||| | | | / ___ |||
/ / ______________________________\\ / / ______________________________\\ / / ______________________________\\ / / ______________________________\\ / ______________________________\ / ______________________________\ | | \\/ -2 + \/ 5 / || | | \\/ -2 + \/ 5 / || | | \\/ -2 + \/ 5 / || | | \\/ -2 + \/ 5 / || | | \\/ -2 + \/ 5 /|| | | \\/ -2 + \/ 5 /|| | | \\/ -2 + \/ 5 /|| | | \\/ -2 + \/ 5 /||
| | / ___________ || | | / ___________ || | | / ___________ || | | / ___________ || | / ___________ | | / ___________ | | | -------------------------|| | | -------------------------|| | | -------------------------|| | | -------------------------|| | | -----------------------|| | | -----------------------|| | | -----------------------|| | | -----------------------||
| | / ___ / ___ || | | / ___ / ___ || | | / ___ / ___ || | | / ___ / ___ || | / ___ / ___ | | / ___ / ___ | | | 2 || | | 2 || | | 2 || | | 2 || | | 2 || | | 2 || | | 2 || | | 2 ||
2*im\atanh\\/ 2 + \/ 5 + 2*\/ 2 + \/ 5 // - 2*I*re\atanh\\/ 2 + \/ 5 + 2*\/ 2 + \/ 5 // + - 2*im\atanh\\/ 2 + \/ 5 + 2*\/ 2 + \/ 5 // + 2*I*re\atanh\\/ 2 + \/ 5 + 2*\/ 2 + \/ 5 // - 2*I*atanh\\/ 2 + \/ 5 - 2*\/ 2 + \/ 5 / + 2*I*atanh\\/ 2 + \/ 5 - 2*\/ 2 + \/ 5 / + - 2*re\atan\e // - 2*I*im\atan\e // + 2*re\atan\e // + 2*I*im\atan\e // + - 2*re\atan\e // - 2*I*im\atan\e // + 2*re\atan\e // + 2*I*im\atan\e //
$$\left(\left(\left(2 \operatorname{re}{\left(\operatorname{atan}{\left(e^{- \frac{i \operatorname{atan}{\left(\frac{2}{\sqrt{-2 + \sqrt{5}}} \right)}}{2}} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(e^{- \frac{i \operatorname{atan}{\left(\frac{2}{\sqrt{-2 + \sqrt{5}}} \right)}}{2}} \right)}\right)}\right) + \left(\left(\left(- 2 i \operatorname{atanh}{\left(\sqrt{- 2 \sqrt{2 + \sqrt{5}} + 2 + \sqrt{5}} \right)} + \left(\left(2 \operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{2 + \sqrt{5} + 2 \sqrt{2 + \sqrt{5}}} \right)}\right)} - 2 i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{2 + \sqrt{5} + 2 \sqrt{2 + \sqrt{5}}} \right)}\right)}\right) + \left(- 2 \operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{2 + \sqrt{5} + 2 \sqrt{2 + \sqrt{5}}} \right)}\right)} + 2 i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{2 + \sqrt{5} + 2 \sqrt{2 + \sqrt{5}}} \right)}\right)}\right)\right)\right) + 2 i \operatorname{atanh}{\left(\sqrt{- 2 \sqrt{2 + \sqrt{5}} + 2 + \sqrt{5}} \right)}\right) + \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(e^{- \frac{i \operatorname{atan}{\left(\frac{2}{\sqrt{-2 + \sqrt{5}}} \right)}}{2}} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(e^{- \frac{i \operatorname{atan}{\left(\frac{2}{\sqrt{-2 + \sqrt{5}}} \right)}}{2}} \right)}\right)}\right)\right)\right) + \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(e^{\frac{i \operatorname{atan}{\left(\frac{2}{\sqrt{-2 + \sqrt{5}}} \right)}}{2}} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(e^{\frac{i \operatorname{atan}{\left(\frac{2}{\sqrt{-2 + \sqrt{5}}} \right)}}{2}} \right)}\right)}\right)\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(e^{\frac{i \operatorname{atan}{\left(\frac{2}{\sqrt{-2 + \sqrt{5}}} \right)}}{2}} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(e^{\frac{i \operatorname{atan}{\left(\frac{2}{\sqrt{-2 + \sqrt{5}}} \right)}}{2}} \right)}\right)}\right)$$
=
0
$$0$$
producto
/ / / / 2 \ \\ / / / 2 \ \\\ / / / / 2 \ \\ / / / 2 \ \\\ / / / / 2 \\\ / / / 2 \\\\ / / / / 2 \\\ / / / 2 \\\\
| | | -I*atan|---------------| || | | -I*atan|---------------| ||| | | | -I*atan|---------------| || | | -I*atan|---------------| ||| | | | I*atan|---------------||| | | I*atan|---------------|||| | | | I*atan|---------------||| | | I*atan|---------------||||
| | | | ____________| || | | | ____________| ||| | | | | ____________| || | | | ____________| ||| | | | | ____________||| | | | ____________|||| | | | | ____________||| | | | ____________||||
| | | | / ___ | || | | | / ___ | ||| | | | | / ___ | || | | | / ___ | ||| | | | | / ___ ||| | | | / ___ |||| | | | | / ___ ||| | | | / ___ ||||
/ / / ______________________________\\ / / ______________________________\\\ / / / ______________________________\\ / / ______________________________\\\ / ______________________________\ / ______________________________\ | | | \\/ -2 + \/ 5 / || | | \\/ -2 + \/ 5 / ||| | | | \\/ -2 + \/ 5 / || | | \\/ -2 + \/ 5 / ||| | | | \\/ -2 + \/ 5 /|| | | \\/ -2 + \/ 5 /||| | | | \\/ -2 + \/ 5 /|| | | \\/ -2 + \/ 5 /|||
| | | / ___________ || | | / ___________ ||| | | | / ___________ || | | / ___________ ||| | / ___________ | | / ___________ | | | | -------------------------|| | | -------------------------||| | | | -------------------------|| | | -------------------------||| | | | -----------------------|| | | -----------------------||| | | | -----------------------|| | | -----------------------|||
| | | / ___ / ___ || | | / ___ / ___ ||| | | | / ___ / ___ || | | / ___ / ___ ||| | / ___ / ___ | | / ___ / ___ | | | | 2 || | | 2 ||| | | | 2 || | | 2 ||| | | | 2 || | | 2 ||| | | | 2 || | | 2 |||
\2*im\atanh\\/ 2 + \/ 5 + 2*\/ 2 + \/ 5 // - 2*I*re\atanh\\/ 2 + \/ 5 + 2*\/ 2 + \/ 5 ///*\- 2*im\atanh\\/ 2 + \/ 5 + 2*\/ 2 + \/ 5 // + 2*I*re\atanh\\/ 2 + \/ 5 + 2*\/ 2 + \/ 5 ///*-2*I*atanh\\/ 2 + \/ 5 - 2*\/ 2 + \/ 5 /*2*I*atanh\\/ 2 + \/ 5 - 2*\/ 2 + \/ 5 /*\- 2*re\atan\e // - 2*I*im\atan\e ///*\2*re\atan\e // + 2*I*im\atan\e ///*\- 2*re\atan\e // - 2*I*im\atan\e ///*\2*re\atan\e // + 2*I*im\atan\e ///
$$2 i \operatorname{atanh}{\left(\sqrt{- 2 \sqrt{2 + \sqrt{5}} + 2 + \sqrt{5}} \right)} - 2 i \operatorname{atanh}{\left(\sqrt{- 2 \sqrt{2 + \sqrt{5}} + 2 + \sqrt{5}} \right)} \left(- 2 \operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{2 + \sqrt{5} + 2 \sqrt{2 + \sqrt{5}}} \right)}\right)} + 2 i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{2 + \sqrt{5} + 2 \sqrt{2 + \sqrt{5}}} \right)}\right)}\right) \left(2 \operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{2 + \sqrt{5} + 2 \sqrt{2 + \sqrt{5}}} \right)}\right)} - 2 i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{2 + \sqrt{5} + 2 \sqrt{2 + \sqrt{5}}} \right)}\right)}\right) \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(e^{- \frac{i \operatorname{atan}{\left(\frac{2}{\sqrt{-2 + \sqrt{5}}} \right)}}{2}} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(e^{- \frac{i \operatorname{atan}{\left(\frac{2}{\sqrt{-2 + \sqrt{5}}} \right)}}{2}} \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(e^{- \frac{i \operatorname{atan}{\left(\frac{2}{\sqrt{-2 + \sqrt{5}}} \right)}}{2}} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(e^{- \frac{i \operatorname{atan}{\left(\frac{2}{\sqrt{-2 + \sqrt{5}}} \right)}}{2}} \right)}\right)}\right) \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(e^{\frac{i \operatorname{atan}{\left(\frac{2}{\sqrt{-2 + \sqrt{5}}} \right)}}{2}} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(e^{\frac{i \operatorname{atan}{\left(\frac{2}{\sqrt{-2 + \sqrt{5}}} \right)}}{2}} \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(e^{\frac{i \operatorname{atan}{\left(\frac{2}{\sqrt{-2 + \sqrt{5}}} \right)}}{2}} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(e^{\frac{i \operatorname{atan}{\left(\frac{2}{\sqrt{-2 + \sqrt{5}}} \right)}}{2}} \right)}\right)}\right)$$
=
2 2
/ / / / 2 \\\ / / / 2 \\\\ / / / / 2 \ \\ / / / 2 \ \\\
| | | I*atan|---------------||| | | I*atan|---------------|||| | | | -I*atan|---------------| || | | -I*atan|---------------| |||
| | | | ____________||| | | | ____________|||| | | | | ____________| || | | | ____________| |||
| | | | / ___ ||| | | | / ___ |||| | | | | / ___ | || | | | / ___ | ||| 2
| | | \\/ -2 + \/ 5 /|| | | \\/ -2 + \/ 5 /||| | | | \\/ -2 + \/ 5 / || | | \\/ -2 + \/ 5 / ||| / / / ______________________________\\ / / ______________________________\\\ / ______________________________\
| | | -----------------------|| | | -----------------------||| | | | -------------------------|| | | -------------------------||| | | | / ___________ || | | / ___________ ||| | / ___________ |
| | | 2 || | | 2 ||| | | | 2 || | | 2 ||| | | | / ___ / ___ || | | / ___ / ___ ||| 2| / ___ / ___ |
-256*\I*im\atan\e // + re\atan\e /// *\I*im\atan\e // + re\atan\e /// *\- I*re\atanh\\/ 2 + \/ 5 + 2*\/ 2 + \/ 5 // + im\atanh\\/ 2 + \/ 5 + 2*\/ 2 + \/ 5 /// *atanh \\/ 2 + \/ 5 - 2*\/ 2 + \/ 5 /
$$- 256 \left(\operatorname{re}{\left(\operatorname{atan}{\left(e^{- \frac{i \operatorname{atan}{\left(\frac{2}{\sqrt{-2 + \sqrt{5}}} \right)}}{2}} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(e^{- \frac{i \operatorname{atan}{\left(\frac{2}{\sqrt{-2 + \sqrt{5}}} \right)}}{2}} \right)}\right)}\right)^{2} \left(\operatorname{re}{\left(\operatorname{atan}{\left(e^{\frac{i \operatorname{atan}{\left(\frac{2}{\sqrt{-2 + \sqrt{5}}} \right)}}{2}} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(e^{\frac{i \operatorname{atan}{\left(\frac{2}{\sqrt{-2 + \sqrt{5}}} \right)}}{2}} \right)}\right)}\right)^{2} \left(\operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{2 + \sqrt{5} + 2 \sqrt{2 + \sqrt{5}}} \right)}\right)} - i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{2 + \sqrt{5} + 2 \sqrt{2 + \sqrt{5}}} \right)}\right)}\right)^{2} \operatorname{atanh}^{2}{\left(\sqrt{- 2 \sqrt{2 + \sqrt{5}} + 2 + \sqrt{5}} \right)}$$
-256*(i*im(atan(exp(i*atan(2/sqrt(-2 + sqrt(5)))/2))) + re(atan(exp(i*atan(2/sqrt(-2 + sqrt(5)))/2))))^2*(i*im(atan(exp(-i*atan(2/sqrt(-2 + sqrt(5)))/2))) + re(atan(exp(-i*atan(2/sqrt(-2 + sqrt(5)))/2))))^2*(-i*re(atanh(sqrt(2 + sqrt(5) + 2*sqrt(2 + sqrt(5))))) + im(atanh(sqrt(2 + sqrt(5) + 2*sqrt(2 + sqrt(5))))))^2*atanh(sqrt(2 + sqrt(5) - 2*sqrt(2 + sqrt(5))))^2
Respuesta rápida
[src]
/ / ______________________________\\ / / ______________________________\\
| | / ___________ || | | / ___________ ||
| | / ___ / ___ || | | / ___ / ___ ||
x1 = 2*im\atanh\\/ 2 + \/ 5 + 2*\/ 2 + \/ 5 // - 2*I*re\atanh\\/ 2 + \/ 5 + 2*\/ 2 + \/ 5 //
$$x_{1} = 2 \operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{2 + \sqrt{5} + 2 \sqrt{2 + \sqrt{5}}} \right)}\right)} - 2 i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{2 + \sqrt{5} + 2 \sqrt{2 + \sqrt{5}}} \right)}\right)}$$
/ / ______________________________\\ / / ______________________________\\
| | / ___________ || | | / ___________ ||
| | / ___ / ___ || | | / ___ / ___ ||
x2 = - 2*im\atanh\\/ 2 + \/ 5 + 2*\/ 2 + \/ 5 // + 2*I*re\atanh\\/ 2 + \/ 5 + 2*\/ 2 + \/ 5 //
$$x_{2} = - 2 \operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{2 + \sqrt{5} + 2 \sqrt{2 + \sqrt{5}}} \right)}\right)} + 2 i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{2 + \sqrt{5} + 2 \sqrt{2 + \sqrt{5}}} \right)}\right)}$$
/ ______________________________\
| / ___________ |
| / ___ / ___ |
x3 = -2*I*atanh\\/ 2 + \/ 5 - 2*\/ 2 + \/ 5 /
$$x_{3} = - 2 i \operatorname{atanh}{\left(\sqrt{- 2 \sqrt{2 + \sqrt{5}} + 2 + \sqrt{5}} \right)}$$
/ ______________________________\
| / ___________ |
| / ___ / ___ |
x4 = 2*I*atanh\\/ 2 + \/ 5 - 2*\/ 2 + \/ 5 /
$$x_{4} = 2 i \operatorname{atanh}{\left(\sqrt{- 2 \sqrt{2 + \sqrt{5}} + 2 + \sqrt{5}} \right)}$$
/ / / 2 \ \\ / / / 2 \ \\
| | -I*atan|---------------| || | | -I*atan|---------------| ||
| | | ____________| || | | | ____________| ||
| | | / ___ | || | | | / ___ | ||
| | \\/ -2 + \/ 5 / || | | \\/ -2 + \/ 5 / ||
| | -------------------------|| | | -------------------------||
| | 2 || | | 2 ||
x5 = - 2*re\atan\e // - 2*I*im\atan\e //
$$x_{5} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(e^{- \frac{i \operatorname{atan}{\left(\frac{2}{\sqrt{-2 + \sqrt{5}}} \right)}}{2}} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(e^{- \frac{i \operatorname{atan}{\left(\frac{2}{\sqrt{-2 + \sqrt{5}}} \right)}}{2}} \right)}\right)}$$
/ / / 2 \ \\ / / / 2 \ \\
| | -I*atan|---------------| || | | -I*atan|---------------| ||
| | | ____________| || | | | ____________| ||
| | | / ___ | || | | | / ___ | ||
| | \\/ -2 + \/ 5 / || | | \\/ -2 + \/ 5 / ||
| | -------------------------|| | | -------------------------||
| | 2 || | | 2 ||
x6 = 2*re\atan\e // + 2*I*im\atan\e //
$$x_{6} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(e^{- \frac{i \operatorname{atan}{\left(\frac{2}{\sqrt{-2 + \sqrt{5}}} \right)}}{2}} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(e^{- \frac{i \operatorname{atan}{\left(\frac{2}{\sqrt{-2 + \sqrt{5}}} \right)}}{2}} \right)}\right)}$$
/ / / 2 \\\ / / / 2 \\\
| | I*atan|---------------||| | | I*atan|---------------|||
| | | ____________||| | | | ____________|||
| | | / ___ ||| | | | / ___ |||
| | \\/ -2 + \/ 5 /|| | | \\/ -2 + \/ 5 /||
| | -----------------------|| | | -----------------------||
| | 2 || | | 2 ||
x7 = - 2*re\atan\e // - 2*I*im\atan\e //
$$x_{7} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(e^{\frac{i \operatorname{atan}{\left(\frac{2}{\sqrt{-2 + \sqrt{5}}} \right)}}{2}} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(e^{\frac{i \operatorname{atan}{\left(\frac{2}{\sqrt{-2 + \sqrt{5}}} \right)}}{2}} \right)}\right)}$$
/ / / 2 \\\ / / / 2 \\\
| | I*atan|---------------||| | | I*atan|---------------|||
| | | ____________||| | | | ____________|||
| | | / ___ ||| | | | / ___ |||
| | \\/ -2 + \/ 5 /|| | | \\/ -2 + \/ 5 /||
| | -----------------------|| | | -----------------------||
| | 2 || | | 2 ||
x8 = 2*re\atan\e // + 2*I*im\atan\e //
$$x_{8} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(e^{\frac{i \operatorname{atan}{\left(\frac{2}{\sqrt{-2 + \sqrt{5}}} \right)}}{2}} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(e^{\frac{i \operatorname{atan}{\left(\frac{2}{\sqrt{-2 + \sqrt{5}}} \right)}}{2}} \right)}\right)}$$
x8 = 2*re(atan(exp(i*atan(2/sqrt(-2 + sqrt(5)))/2))) + 2*i*im(atan(exp(i*atan(2/sqrt(-2 + sqrt(5)))/2)))
Respuesta numérica
[src]
x1 = -3.14159265358979 - 0.721817737589405*i
x2 = 3.14159265358979 + 0.721817737589405*i
x3 = -0.721817737589405*i
x4 = 0.721817737589405*i
x5 = -1.5707963267949 + 0.721817737589405*i
x6 = 1.5707963267949 - 0.721817737589405*i
x7 = -1.5707963267949 - 0.721817737589405*i
x8 = 1.5707963267949 + 0.721817737589405*i
x8 = 1.5707963267949 + 0.721817737589405*i