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- La ecuación:
-
Ecuación x^4+2*x^2-8=0
-
Ecuación x*(x^2+8*x+16)=5*(x+4)
-
Ecuación -25-x=-17
-
Ecuación x^2+3x=4
- Expresar {x} en función de y en la ecuación:
- -18*x-2*y=9
- -14*x+10*y=19
- -9*x+1*y=3
- -17*x+1*y=-11
- Integral de d{x}:
- sin(2*x)
- Gráfico de la función y =:
-
sin(2*x)
- Derivada de:
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sin(2*x)
-
Expresiones idénticas
- uno +(sin(x))^ dos =sin(dos *x)
- 1 más ( seno de (x)) al cuadrado es igual a seno de (2 multiplicar por x)
- uno más ( seno de (x)) en el grado dos es igual a seno de (dos multiplicar por x)
- 1+(sin(x))2=sin(2*x)
- 1+sinx2=sin2*x
- 1+(sin(x))²=sin(2*x)
- 1+(sin(x)) en el grado 2=sin(2*x)
- 1+(sin(x))^2=sin(2x)
- 1+(sin(x))2=sin(2x)
- 1+sinx2=sin2x
- 1+sinx^2=sin2x
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Expresiones semejantes
- sin2x+1=cosx+2sinx
- sin2x=1
- 1-(sin(x))^2=sin(2*x)
- sin2x=1/2
- 3*exp(-7x)*sin(2x+0.1)-1=0
- 1+(sinx)^2=sin(2*x)
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Expresiones con funciones
- Seno sin
- sin(x)=1,5
- sin(x-1)=0
- sin2x=1
- sin(3*x)=-1/2
- sin(3*x)=-1
- Seno sin
- sin(x)=1,5
- sin(x-1)=0
- sin2x=1
- sin(3*x)=-1/2
- sin(3*x)=-1
1+(sin(x))^2=sin(2*x) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 1 + sin (x) = sin(2*x)
$$\sin^{2}{\left(x \right)} + 1 = \sin{\left(2 x \right)}$$
Respuesta rápida
[src]
/ /atan(2)\\
|sin|-------||
/log(5) /4 ___\\ | \ 2 /|
x1 = -pi + I*|------ - log\\/ 5 /| + atan|------------|
\ 2 / | /atan(2)\|
|cos|-------||
\ \ 2 //
$$x_{1} = - \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(2 \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(2 \right)}}{2} \right)}} \right)} + i \left(- \log{\left(\sqrt[4]{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)$$
/ / ___\\
atan(2) |log(5) log\\/ 5 /|
x2 = ------- + I*|------ - ----------|
2 \ 2 2 /
$$x_{2} = \frac{\operatorname{atan}{\left(2 \right)}}{2} + i \left(- \frac{\log{\left(\sqrt{5} \right)}}{2} + \frac{\log{\left(5 \right)}}{2}\right)$$
/ /atan(2)\\
|sin|-------||
/4 ___\ | \ 2 /|
x3 = -pi - I*log\\/ 5 / + atan|------------|
| /atan(2)\|
|cos|-------||
\ \ 2 //
$$x_{3} = - \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(2 \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(2 \right)}}{2} \right)}} \right)} - i \log{\left(\sqrt[4]{5} \right)}$$
/ ___\
atan(2) I*log\\/ 5 /
x4 = ------- - ------------
2 2
$$x_{4} = \frac{\operatorname{atan}{\left(2 \right)}}{2} - \frac{i \log{\left(\sqrt{5} \right)}}{2}$$
x4 = atan(2)/2 - i*log(sqrt(5))/2
Suma y producto de raíces
[src]
suma
/ /atan(2)\\ / /atan(2)\\
|sin|-------|| / / ___\\ |sin|-------|| / ___\
/log(5) /4 ___\\ | \ 2 /| atan(2) |log(5) log\\/ 5 /| /4 ___\ | \ 2 /| atan(2) I*log\\/ 5 /
-pi + I*|------ - log\\/ 5 /| + atan|------------| + ------- + I*|------ - ----------| + -pi - I*log\\/ 5 / + atan|------------| + ------- - ------------
\ 2 / | /atan(2)\| 2 \ 2 2 / | /atan(2)\| 2 2
|cos|-------|| |cos|-------||
\ \ 2 // \ \ 2 //
$$\left(\frac{\operatorname{atan}{\left(2 \right)}}{2} - \frac{i \log{\left(\sqrt{5} \right)}}{2}\right) + \left(\left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(2 \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(2 \right)}}{2} \right)}} \right)} - i \log{\left(\sqrt[4]{5} \right)}\right) + \left(\left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(2 \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(2 \right)}}{2} \right)}} \right)} + i \left(- \log{\left(\sqrt[4]{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)\right) + \left(\frac{\operatorname{atan}{\left(2 \right)}}{2} + i \left(- \frac{\log{\left(\sqrt{5} \right)}}{2} + \frac{\log{\left(5 \right)}}{2}\right)\right)\right)\right)$$
=
/ /atan(2)\\
|sin|-------|| / / ___\\ / ___\
| \ 2 /| /log(5) /4 ___\\ |log(5) log\\/ 5 /| /4 ___\ I*log\\/ 5 /
-2*pi + 2*atan|------------| + I*|------ - log\\/ 5 /| + I*|------ - ----------| - I*log\\/ 5 / - ------------ + atan(2)
| /atan(2)\| \ 2 / \ 2 2 / 2
|cos|-------||
\ \ 2 //
$$- 2 \pi + 2 \operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(2 \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(2 \right)}}{2} \right)}} \right)} + \operatorname{atan}{\left(2 \right)} - i \log{\left(\sqrt[4]{5} \right)} - \frac{i \log{\left(\sqrt{5} \right)}}{2} + i \left(- \log{\left(\sqrt[4]{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right) + i \left(- \frac{\log{\left(\sqrt{5} \right)}}{2} + \frac{\log{\left(5 \right)}}{2}\right)$$
producto
/ / /atan(2)\\\ / / /atan(2)\\\ | |sin|-------||| / / / ___\\\ | |sin|-------||| / / ___\\ | /log(5) /4 ___\\ | \ 2 /|| |atan(2) |log(5) log\\/ 5 /|| | /4 ___\ | \ 2 /|| |atan(2) I*log\\/ 5 /| |-pi + I*|------ - log\\/ 5 /| + atan|------------||*|------- + I*|------ - ----------||*|-pi - I*log\\/ 5 / + atan|------------||*|------- - ------------| | \ 2 / | /atan(2)\|| \ 2 \ 2 2 // | | /atan(2)\|| \ 2 2 / | |cos|-------||| | |cos|-------||| \ \ \ 2 /// \ \ \ 2 ///
$$\left(\frac{\operatorname{atan}{\left(2 \right)}}{2} + i \left(- \frac{\log{\left(\sqrt{5} \right)}}{2} + \frac{\log{\left(5 \right)}}{2}\right)\right) \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(2 \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(2 \right)}}{2} \right)}} \right)} + i \left(- \log{\left(\sqrt[4]{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)\right) \left(- \pi + \operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(2 \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(2 \right)}}{2} \right)}} \right)} - i \log{\left(\sqrt[4]{5} \right)}\right) \left(\frac{\operatorname{atan}{\left(2 \right)}}{2} - \frac{i \log{\left(\sqrt{5} \right)}}{2}\right)$$
=
4 4 3 2 2 2 2 2 2 2 atan (2) log (5) pi*atan (2) pi *atan (2) pi *log (5) atan (2)*log (5) pi*log (5)*atan(2) -------- + ------- - ----------- + ------------ + ----------- + ---------------- - ------------------ 16 256 4 4 16 32 16
$$- \frac{\pi \operatorname{atan}^{3}{\left(2 \right)}}{4} - \frac{\pi \log{\left(5 \right)}^{2} \operatorname{atan}{\left(2 \right)}}{16} + \frac{\log{\left(5 \right)}^{4}}{256} + \frac{\operatorname{atan}^{4}{\left(2 \right)}}{16} + \frac{\log{\left(5 \right)}^{2} \operatorname{atan}^{2}{\left(2 \right)}}{32} + \frac{\pi^{2} \log{\left(5 \right)}^{2}}{16} + \frac{\pi^{2} \operatorname{atan}^{2}{\left(2 \right)}}{4}$$
atan(2)^4/16 + log(5)^4/256 - pi*atan(2)^3/4 + pi^2*atan(2)^2/4 + pi^2*log(5)^2/16 + atan(2)^2*log(5)^2/32 - pi*log(5)^2*atan(2)/16
Respuesta numérica
[src]
x1 = -2.58801829469275 + 0.402359478108525*i
x2 = 0.553574358897045 + 0.402359478108525*i
x3 = -2.58801829469275 - 0.402359478108525*i
x4 = 0.553574358897045 - 0.402359478108525*i
x4 = 0.553574358897045 - 0.402359478108525*i