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sinpi((x+11)/6)=-1/2 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
         x + 11       
sin(p)*I*------ = -1/2
           6
x+116isin⁡(p)=−12\frac{x + 11}{6} i \sin{\left(p \right)} = - \frac{1}{2}
Simplificar
Solución detallada
Tenemos la ecuación
x+116isin⁡(p)=−12\frac{x + 11}{6} i \sin{\left(p \right)} = - \frac{1}{2}
cambiamos
i(x+11)sin⁡(p)6−12=0\frac{i \left(x + 11\right) \sin{\left(p \right)}}{6} - \frac{1}{2} = 0
x+116isin⁡(p)−12=0\frac{x + 11}{6} i \sin{\left(p \right)} - \frac{1}{2} = 0
Sustituimos
w=sin⁡(p)w = \sin{\left(p \right)}
Abrimos los paréntesis en el miembro izquierdo de la ecuación
-1/2 + i*wx/6+11/6 = 0

Sumamos los términos semejantes en el miembro izquierdo de la ecuación:
-1/2 + i*w*(11 + x)/6 = 0

Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
iw(x+11)6=12\frac{i w \left(x + 11\right)}{6} = \frac{1}{2}
Dividamos ambos miembros de la ecuación en i*(11 + x)/6
w = 1/2 / (i*(11 + x)/6)

Obtenemos la respuesta: w = -3*i/(11 + x)
hacemos cambio inverso
sin⁡(p)=w\sin{\left(p \right)} = w
sustituimos w:
Gráfica
Suma y producto de raíces [src] 
suma
                    3*cos(re(p))*sinh(im(p))                             3*I*cosh(im(p))*sin(re(p))            
-11 + --------------------------------------------------- + ---------------------------------------------------
         2            2              2           2             2            2              2           2       
      cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))   cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))
−11+3isin⁡(re⁡(p))cosh⁡(im⁡(p))sin⁡2(re⁡(p))cosh⁡2(im⁡(p))+cos⁡2(re⁡(p))sinh⁡2(im⁡(p))+3cos⁡(re⁡(p))sinh⁡(im⁡(p))sin⁡2(re⁡(p))cosh⁡2(im⁡(p))+cos⁡2(re⁡(p))sinh⁡2(im⁡(p))-11 + \frac{3 i \sin{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} + \frac{3 \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} 
=
                    3*cos(re(p))*sinh(im(p))                             3*I*cosh(im(p))*sin(re(p))            
-11 + --------------------------------------------------- + ---------------------------------------------------
         2            2              2           2             2            2              2           2       
      cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))   cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))
−11+3isin⁡(re⁡(p))cosh⁡(im⁡(p))sin⁡2(re⁡(p))cosh⁡2(im⁡(p))+cos⁡2(re⁡(p))sinh⁡2(im⁡(p))+3cos⁡(re⁡(p))sinh⁡(im⁡(p))sin⁡2(re⁡(p))cosh⁡2(im⁡(p))+cos⁡2(re⁡(p))sinh⁡2(im⁡(p))-11 + \frac{3 i \sin{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} + \frac{3 \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} 
producto
                    3*cos(re(p))*sinh(im(p))                             3*I*cosh(im(p))*sin(re(p))            
-11 + --------------------------------------------------- + ---------------------------------------------------
         2            2              2           2             2            2              2           2       
      cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))   cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))
−11+3isin⁡(re⁡(p))cosh⁡(im⁡(p))sin⁡2(re⁡(p))cosh⁡2(im⁡(p))+cos⁡2(re⁡(p))sinh⁡2(im⁡(p))+3cos⁡(re⁡(p))sinh⁡(im⁡(p))sin⁡2(re⁡(p))cosh⁡2(im⁡(p))+cos⁡2(re⁡(p))sinh⁡2(im⁡(p))-11 + \frac{3 i \sin{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} + \frac{3 \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} 
=
-(I*(-3 + 11*cos(re(p))*sinh(im(p))) + 11*cosh(im(p))*sin(re(p))) 
------------------------------------------------------------------
        cosh(im(p))*sin(re(p)) + I*cos(re(p))*sinh(im(p))
−i(11cos⁡(re⁡(p))sinh⁡(im⁡(p))−3)+11sin⁡(re⁡(p))cosh⁡(im⁡(p))sin⁡(re⁡(p))cosh⁡(im⁡(p))+icos⁡(re⁡(p))sinh⁡(im⁡(p))- \frac{i \left(11 \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)} - 3\right) + 11 \sin{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)} + i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}} 
-(i*(-3 + 11*cos(re(p))*sinh(im(p))) + 11*cosh(im(p))*sin(re(p)))/(cosh(im(p))*sin(re(p)) + i*cos(re(p))*sinh(im(p)))
Respuesta rápida [src] 
                         3*cos(re(p))*sinh(im(p))                             3*I*cosh(im(p))*sin(re(p))            
x1 = -11 + --------------------------------------------------- + ---------------------------------------------------
              2            2              2           2             2            2              2           2       
           cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))   cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))
x1=−11+3isin⁡(re⁡(p))cosh⁡(im⁡(p))sin⁡2(re⁡(p))cosh⁡2(im⁡(p))+cos⁡2(re⁡(p))sinh⁡2(im⁡(p))+3cos⁡(re⁡(p))sinh⁡(im⁡(p))sin⁡2(re⁡(p))cosh⁡2(im⁡(p))+cos⁡2(re⁡(p))sinh⁡2(im⁡(p))x_{1} = -11 + \frac{3 i \sin{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} + \frac{3 \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} 
x1 = -11 + 3*i*sin(re(p))*cosh(im(p))/(sin(re(p))^2*cosh(im(p))^2 + cos(re(p))^2*sinh(im(p))^2) + 3*cos(re(p))*sinh(im(p))/(sin(re(p))^2*cosh(im(p))^2 + cos(re(p))^2*sinh(im(p))^2)
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