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Otras calculadoras
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- La ecuación:
-
Ecuación |x^2-1|-|x-3|=7
-
Ecuación 2^2-x-1=x^2-5*x-(-1-x^2)
-
Ecuación x^4=(4*x-21)^2
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Ecuación x^2+9=(x+9)^2
- Expresar {x} en función de y en la ecuación:
- 15*x+15*y=16
- -13*x+9*y=1
- -18*x-1*y=-11
- 4*x-7*y=12
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Expresiones idénticas
- cospi(cuatro x+ ciento treinta y dos)/4=-sqrt(dos)/ dos
- coseno de número pi (4x más 132) dividir por 4 es igual a menos raíz cuadrada de (2) dividir por 2
- coseno de número pi (cuatro x más ciento treinta y dos) dividir por 4 es igual a menos raíz cuadrada de (dos) dividir por dos
- cospi(4x+132)/4=-√(2)/2
- cospi4x+132/4=-sqrt2/2
- cospi(4x+132) dividir por 4=-sqrt(2) dividir por 2
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Expresiones semejantes
- cos*((pi(4x+48))/4)=-(sqrt(2)/2)
- cos((pi*(4x+60))/4)=-(sqrt(2)/2)
- cospi(4x+132)/4=+sqrt(2)/2
- cospi(4x-132)/4=-sqrt(2)/2
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Expresiones con funciones
- cospi
- cospi(x+1)/4=√2/2
- cospi(4*x-6)/3=12
- cospi(4x-7)/6=sqrt(3)/2
- cospix=-2
- cospix=6
- Raíz cuadrada sqrt
- sqrt(x+10)=x-2
- sqrt(4x^2-9x+2)=x-2
- sqrt(3x^2-128)=-x
- sqrt(x-5)=x-7
- sqrt(5x+2)-sqrt(5x-10)=2
cospi(4x+132)/4=-sqrt(2)/2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
___
cos(p)*I*(4*x + 132) -\/ 2
-------------------- = -------
4 2
$$\frac{i \cos{\left(p \right)} \left(4 x + 132\right)}{4} = \frac{\left(-1\right) \sqrt{2}}{2}$$
Solución detallada
Tenemos la ecuación
$$\frac{i \cos{\left(p \right)} \left(4 x + 132\right)}{4} = \frac{\left(-1\right) \sqrt{2}}{2}$$
cambiamos
$$i \left(x + 33\right) \cos{\left(p \right)} - 1 + \frac{\sqrt{2}}{2} = 0$$
$$\frac{i \cos{\left(p \right)} \left(4 x + 132\right)}{4} - 1 - \frac{\left(-1\right) \sqrt{2}}{2} = 0$$
Sustituimos
$$w = \cos{\left(p \right)}$$
Abrimos los paréntesis en el miembro izquierdo de la ecuación
Sumamos los términos semejantes en el miembro izquierdo de la ecuación:
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$\frac{i w \left(4 x + 132\right)}{4} + \frac{\sqrt{2}}{2} = 1$$
Dividamos ambos miembros de la ecuación en (sqrt(2)/2 + i*w*(132 + 4*x)/4)/w
Obtenemos la respuesta: w = i*(-2 + sqrt(2))/(2*(33 + x))
hacemos cambio inverso
$$\cos{\left(p \right)} = w$$
sustituimos w:
$$\frac{i \cos{\left(p \right)} \left(4 x + 132\right)}{4} = \frac{\left(-1\right) \sqrt{2}}{2}$$
cambiamos
$$i \left(x + 33\right) \cos{\left(p \right)} - 1 + \frac{\sqrt{2}}{2} = 0$$
$$\frac{i \cos{\left(p \right)} \left(4 x + 132\right)}{4} - 1 - \frac{\left(-1\right) \sqrt{2}}{2} = 0$$
Sustituimos
$$w = \cos{\left(p \right)}$$
Abrimos los paréntesis en el miembro izquierdo de la ecuación
-1 - -sqrt+2)/2 + i*w4*x/4+132/4 = 0
Sumamos los términos semejantes en el miembro izquierdo de la ecuación:
-1 + sqrt(2)/2 + i*w*(132 + 4*x)/4 = 0
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$\frac{i w \left(4 x + 132\right)}{4} + \frac{\sqrt{2}}{2} = 1$$
Dividamos ambos miembros de la ecuación en (sqrt(2)/2 + i*w*(132 + 4*x)/4)/w
w = 1 / ((sqrt(2)/2 + i*w*(132 + 4*x)/4)/w)
Obtenemos la respuesta: w = i*(-2 + sqrt(2))/(2*(33 + x))
hacemos cambio inverso
$$\cos{\left(p \right)} = w$$
sustituimos w:
Gráfica
Respuesta rápida
[src]
___ ___
\/ 2 *sin(re(p))*sinh(im(p)) I*\/ 2 *cos(re(p))*cosh(im(p))
x1 = -33 - ------------------------------------------------------- + -------------------------------------------------------
/ 2 2 2 2 \ / 2 2 2 2 \
2*\cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))/ 2*\cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))/
$$x_{1} = -33 - \frac{\sqrt{2} \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)} + \frac{\sqrt{2} i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)}$$
x1 = -33 - sqrt(2)*sin(re(p))*sinh(im(p))/(2*(sin(re(p))^2*sinh(im(p))^2 + cos(re(p))^2*cosh(im(p))^2)) + sqrt(2)*i*cos(re(p))*cosh(im(p))/(2*(sin(re(p))^2*sinh(im(p))^2 + cos(re(p))^2*cosh(im(p))^2))
Suma y producto de raíces
[src]
suma
___ ___
\/ 2 *sin(re(p))*sinh(im(p)) I*\/ 2 *cos(re(p))*cosh(im(p))
-33 - ------------------------------------------------------- + -------------------------------------------------------
/ 2 2 2 2 \ / 2 2 2 2 \
2*\cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))/ 2*\cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))/
$$-33 - \frac{\sqrt{2} \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)} + \frac{\sqrt{2} i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)}$$
=
___ ___
\/ 2 *sin(re(p))*sinh(im(p)) I*\/ 2 *cos(re(p))*cosh(im(p))
-33 - ------------------------------------------------------- + -------------------------------------------------------
/ 2 2 2 2 \ / 2 2 2 2 \
2*\cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))/ 2*\cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))/
$$-33 - \frac{\sqrt{2} \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)} + \frac{\sqrt{2} i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)}$$
producto
___ ___
\/ 2 *sin(re(p))*sinh(im(p)) I*\/ 2 *cos(re(p))*cosh(im(p))
-33 - ------------------------------------------------------- + -------------------------------------------------------
/ 2 2 2 2 \ / 2 2 2 2 \
2*\cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))/ 2*\cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))/
$$-33 - \frac{\sqrt{2} \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)} + \frac{\sqrt{2} i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{2 \left(\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}\right)}$$
=
/ / ___ \ \
| |\/ 2 | |
-|I*|----- + 33*sin(re(p))*sinh(im(p))| - 33*cos(re(p))*cosh(im(p))|
\ \ 2 / /
---------------------------------------------------------------------
-cos(re(p))*cosh(im(p)) + I*sin(re(p))*sinh(im(p))
$$- \frac{i \left(33 \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)} + \frac{\sqrt{2}}{2}\right) - 33 \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{i \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)} - \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}$$
-(i*(sqrt(2)/2 + 33*sin(re(p))*sinh(im(p))) - 33*cos(re(p))*cosh(im(p)))/(-cos(re(p))*cosh(im(p)) + i*sin(re(p))*sinh(im(p)))