Sr Examen
Otras calculadoras
-
¿Cómo usar?
- La ecuación:
-
Ecuación 6*x^2+x-7=0
-
Ecuación 2-5(3+2x)=17
-
Ecuación (6*x+8)/2+5=5*x/3
-
Ecuación 2,6x-0,75=0,9x-35,6
- Expresar {x} en función de y en la ecuación:
- -9*x-12*y=-19
- -8*x+3*y=-4
- 10*x+3*y=2
- -10*x-12*y=-10
- Gráfico de la función y =:
-
sin(cos(x))
- Integral de d{x}:
- sin(cos(x))
- Derivada de:
-
sin(cos(x))
-
Expresiones idénticas
- sin(cos(x))= dos
- seno de ( coseno de (x)) es igual a 2
- seno de ( coseno de (x)) es igual a dos
- sincosx=2
-
Expresiones semejantes
- sin(cosx)=2
-
Expresiones con funciones
- Seno sin
- sin2x-3sinx-a=|sin2x+sinx+a|
- sin2x+4((cosx)^2)=1
- sin^2x-0.5sinx-0.5=0
- sin((3*pi)/x^2)=-1/2
- sin(2x)=0.96
- Coseno cos
- cos(2pi×x)-3sin(pi×x)+1=0
- cos(x+(|x|))=1
- cos(x-3/4)=0
- cos(x)=-0,7
- cos(y)=x-3
sin(cos(x))=2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Tenemos la ecuación
$$\sin{\left(\cos{\left(x \right)} \right)} = 2$$
cambiamos
$$\sin{\left(\cos{\left(x \right)} \right)} - 2 = 0$$
$$\sin{\left(\cos{\left(x \right)} \right)} - 2 = 0$$
Sustituimos
$$w = \sin{\left(\cos{\left(x \right)} \right)}$$
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$w = 2$$
Obtenemos la respuesta: w = 2
hacemos cambio inverso
$$\sin{\left(\cos{\left(x \right)} \right)} = w$$
sustituimos w:
$$\sin{\left(\cos{\left(x \right)} \right)} = 2$$
cambiamos
$$\sin{\left(\cos{\left(x \right)} \right)} - 2 = 0$$
$$\sin{\left(\cos{\left(x \right)} \right)} - 2 = 0$$
Sustituimos
$$w = \sin{\left(\cos{\left(x \right)} \right)}$$
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$w = 2$$
Obtenemos la respuesta: w = 2
hacemos cambio inverso
$$\sin{\left(\cos{\left(x \right)} \right)} = w$$
sustituimos w:
Respuesta rápida
[src]
x1 = -re(acos(pi - asin(2))) + 2*pi - I*im(acos(pi - asin(2)))
$$x_{1} = - \operatorname{re}{\left(\operatorname{acos}{\left(\pi - \operatorname{asin}{\left(2 \right)} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\pi - \operatorname{asin}{\left(2 \right)} \right)}\right)}$$
x2 = -re(acos(asin(2))) + 2*pi - I*im(acos(asin(2)))
$$x_{2} = - \operatorname{re}{\left(\operatorname{acos}{\left(\operatorname{asin}{\left(2 \right)} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\operatorname{asin}{\left(2 \right)} \right)}\right)}$$
x3 = I*im(acos(pi - asin(2))) + re(acos(pi - asin(2)))
$$x_{3} = \operatorname{re}{\left(\operatorname{acos}{\left(\pi - \operatorname{asin}{\left(2 \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\pi - \operatorname{asin}{\left(2 \right)} \right)}\right)}$$
x4 = I*im(acos(asin(2))) + re(acos(asin(2)))
$$x_{4} = \operatorname{re}{\left(\operatorname{acos}{\left(\operatorname{asin}{\left(2 \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\operatorname{asin}{\left(2 \right)} \right)}\right)}$$
x4 = re(acos(asin(2))) + i*im(acos(asin(2)))
Suma y producto de raíces
[src]
suma
-re(acos(pi - asin(2))) + 2*pi - I*im(acos(pi - asin(2))) + -re(acos(asin(2))) + 2*pi - I*im(acos(asin(2))) + I*im(acos(pi - asin(2))) + re(acos(pi - asin(2))) + I*im(acos(asin(2))) + re(acos(asin(2)))
$$\left(\left(\operatorname{re}{\left(\operatorname{acos}{\left(\pi - \operatorname{asin}{\left(2 \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\pi - \operatorname{asin}{\left(2 \right)} \right)}\right)}\right) + \left(\left(- \operatorname{re}{\left(\operatorname{acos}{\left(\operatorname{asin}{\left(2 \right)} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\operatorname{asin}{\left(2 \right)} \right)}\right)}\right) + \left(- \operatorname{re}{\left(\operatorname{acos}{\left(\pi - \operatorname{asin}{\left(2 \right)} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\pi - \operatorname{asin}{\left(2 \right)} \right)}\right)}\right)\right)\right) + \left(\operatorname{re}{\left(\operatorname{acos}{\left(\operatorname{asin}{\left(2 \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\operatorname{asin}{\left(2 \right)} \right)}\right)}\right)$$
=
4*pi
$$4 \pi$$
producto
(-re(acos(pi - asin(2))) + 2*pi - I*im(acos(pi - asin(2))))*(-re(acos(asin(2))) + 2*pi - I*im(acos(asin(2))))*(I*im(acos(pi - asin(2))) + re(acos(pi - asin(2))))*(I*im(acos(asin(2))) + re(acos(asin(2))))
$$\left(- \operatorname{re}{\left(\operatorname{acos}{\left(\pi - \operatorname{asin}{\left(2 \right)} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\pi - \operatorname{asin}{\left(2 \right)} \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{acos}{\left(\operatorname{asin}{\left(2 \right)} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\operatorname{asin}{\left(2 \right)} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(\pi - \operatorname{asin}{\left(2 \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\pi - \operatorname{asin}{\left(2 \right)} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(\operatorname{asin}{\left(2 \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\operatorname{asin}{\left(2 \right)} \right)}\right)}\right)$$
=
(I*im(acos(pi - asin(2))) + re(acos(pi - asin(2))))*(I*im(acos(asin(2))) + re(acos(asin(2))))*(-2*pi + I*im(acos(pi - asin(2))) + re(acos(pi - asin(2))))*(-2*pi + I*im(acos(asin(2))) + re(acos(asin(2))))
$$\left(\operatorname{re}{\left(\operatorname{acos}{\left(\pi - \operatorname{asin}{\left(2 \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\pi - \operatorname{asin}{\left(2 \right)} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(\operatorname{asin}{\left(2 \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\operatorname{asin}{\left(2 \right)} \right)}\right)}\right) \left(- 2 \pi + \operatorname{re}{\left(\operatorname{acos}{\left(\pi - \operatorname{asin}{\left(2 \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\pi - \operatorname{asin}{\left(2 \right)} \right)}\right)}\right) \left(- 2 \pi + \operatorname{re}{\left(\operatorname{acos}{\left(\operatorname{asin}{\left(2 \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\operatorname{asin}{\left(2 \right)} \right)}\right)}\right)$$
(i*im(acos(pi - asin(2))) + re(acos(pi - asin(2))))*(i*im(acos(asin(2))) + re(acos(asin(2))))*(-2*pi + i*im(acos(pi - asin(2))) + re(acos(pi - asin(2))))*(-2*pi + i*im(acos(asin(2))) + re(acos(asin(2))))
Respuesta numérica
[src]
x1 = 5.52571620207393 + 1.40576484521948*i
x2 = 5.52571620207393 - 1.40576484521948*i
x3 = 0.757469105105656 - 1.40576484521948*i
x4 = 0.757469105105656 + 1.40576484521948*i
x4 = 0.757469105105656 + 1.40576484521948*i