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Otras calculadoras
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- La ecuación:
-
Ecuación x=(x+1)/2
- Ecuación (x-6)(-5x-9)=0
-
Ecuación x^2-14*x+33=0
-
Ecuación x^2-5x=14
- Expresar {x} en función de y en la ecuación:
- 12*x+1*y=15
- -17*x-12*y=-9
- 18*x+17*y=-14
- 16*x-17*y=-15
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Expresiones idénticas
- cosπ(dos x+ treinta)/ cuatro =-√ dos /2
- coseno de π(2x más 30) dividir por 4 es igual a menos √2 dividir por 2
- coseno de π(dos x más treinta) dividir por cuatro es igual a menos √ dos dividir por 2
- cosπ2x+30/4=-√2/2
- cosπ(2x+30) dividir por 4=-√2 dividir por 2
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Expresiones semejantes
- cosπ(2x+30)/4=+√2/2
- cos(π(2x+30))/4=–(√2/2)
- cosπ(2x-30)/4=-√2/2
cosπ(2x+30)/4=-√2/2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
___
cos(p)*I*(2*x + 30) -\/ 2
------------------- = -------
4 2
$$\frac{i \cos{\left(p \right)} \left(2 x + 30\right)}{4} = \frac{\left(-1\right) \sqrt{2}}{2}$$
Solución detallada
Tenemos la ecuación
$$\frac{i \cos{\left(p \right)} \left(2 x + 30\right)}{4} = \frac{\left(-1\right) \sqrt{2}}{2}$$
cambiamos
$$\frac{i \left(x + 15\right) \cos{\left(p \right)}}{2} - 1 + \frac{\sqrt{2}}{2} = 0$$
$$\frac{i \cos{\left(p \right)} \left(2 x + 30\right)}{4} - 1 - \frac{\left(-1\right) \sqrt{2}}{2} = 0$$
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:
$$\frac{i w \left(2 x + 30\right)}{4} + \frac{\sqrt{2}}{2} = 1$$
Dividamos ambos miembros de la ecuación en (sqrt(2)/2 + i*w*(30 + 2*x)/4)/w
Obtenemos la respuesta: w = i*(-2 + sqrt(2))/(15 + x)
hacemos cambio inverso
$$\cos{\left(p \right)} = w$$
sustituimos w:
$$\frac{i \cos{\left(p \right)} \left(2 x + 30\right)}{4} = \frac{\left(-1\right) \sqrt{2}}{2}$$
cambiamos
$$\frac{i \left(x + 15\right) \cos{\left(p \right)}}{2} - 1 + \frac{\sqrt{2}}{2} = 0$$
$$\frac{i \cos{\left(p \right)} \left(2 x + 30\right)}{4} - 1 - \frac{\left(-1\right) \sqrt{2}}{2} = 0$$
Sustituimos
$$w = \cos{\left(p \right)}$$
Abrimos los paréntesis en el miembro izquierdo de la ecuación
-1 - -sqrt+2)/2 + i*w2*x/4+30/4 = 0
Sumamos los términos semejantes en el miembro izquierdo de la ecuación:
-1 + sqrt(2)/2 + i*w*(30 + 2*x)/4 = 0
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$\frac{i w \left(2 x + 30\right)}{4} + \frac{\sqrt{2}}{2} = 1$$
Dividamos ambos miembros de la ecuación en (sqrt(2)/2 + i*w*(30 + 2*x)/4)/w
w = 1 / ((sqrt(2)/2 + i*w*(30 + 2*x)/4)/w)
Obtenemos la respuesta: w = i*(-2 + sqrt(2))/(15 + x)
hacemos cambio inverso
$$\cos{\left(p \right)} = w$$
sustituimos w:
Gráfica
Suma y producto de raíces
[src]
suma
___ ___
\/ 2 *sin(re(p))*sinh(im(p)) I*\/ 2 *cos(re(p))*cosh(im(p))
-15 - --------------------------------------------------- + ---------------------------------------------------
2 2 2 2 2 2 2 2
cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p)) cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))
$$-15 - \frac{\sqrt{2} \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} + \frac{\sqrt{2} i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}}$$
=
___ ___
\/ 2 *sin(re(p))*sinh(im(p)) I*\/ 2 *cos(re(p))*cosh(im(p))
-15 - --------------------------------------------------- + ---------------------------------------------------
2 2 2 2 2 2 2 2
cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p)) cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))
$$-15 - \frac{\sqrt{2} \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} + \frac{\sqrt{2} i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}}$$
producto
___ ___
\/ 2 *sin(re(p))*sinh(im(p)) I*\/ 2 *cos(re(p))*cosh(im(p))
-15 - --------------------------------------------------- + ---------------------------------------------------
2 2 2 2 2 2 2 2
cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p)) cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))
$$-15 - \frac{\sqrt{2} \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} + \frac{\sqrt{2} i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}}$$
=
/ / ___ \ \
-\I*\\/ 2 + 15*sin(re(p))*sinh(im(p))/ - 15*cos(re(p))*cosh(im(p))/
---------------------------------------------------------------------
-cos(re(p))*cosh(im(p)) + I*sin(re(p))*sinh(im(p))
$$- \frac{i \left(15 \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)} + \sqrt{2}\right) - 15 \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{i \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)} - \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}$$
-(i*(sqrt(2) + 15*sin(re(p))*sinh(im(p))) - 15*cos(re(p))*cosh(im(p)))/(-cos(re(p))*cosh(im(p)) + i*sin(re(p))*sinh(im(p)))
Respuesta rápida
[src]
___ ___
\/ 2 *sin(re(p))*sinh(im(p)) I*\/ 2 *cos(re(p))*cosh(im(p))
x1 = -15 - --------------------------------------------------- + ---------------------------------------------------
2 2 2 2 2 2 2 2
cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p)) cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))
$$x_{1} = -15 - \frac{\sqrt{2} \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} + \frac{\sqrt{2} i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}}$$
x1 = -15 - sqrt(2)*sin(re(p))*sinh(im(p))/(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))/(sin(re(p))^2*sinh(im(p))^2 + cos(re(p))^2*cosh(im(p))^2)