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Csin(x)−2. la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
c*sin(x) - 2 = 0
csin⁡(x)−2=0c \sin{\left(x \right)} - 2 = 0
Simplificar
Solución detallada
Tenemos la ecuación
csin⁡(x)−2=0c \sin{\left(x \right)} - 2 = 0
es la ecuación trigonométrica más simple
Transportemos -2 al miembro derecho de la ecuación

cambiando el signo de -2

Obtenemos:
csin⁡(x)=2c \sin{\left(x \right)} = 2
Dividamos ambos miembros de la ecuación en c

La ecuación se convierte en
sin⁡(x)=2c\sin{\left(x \right)} = \frac{2}{c}
Esta ecuación se reorganiza en
x=2πn+asin⁡(2c)x = 2 \pi n + \operatorname{asin}{\left(\frac{2}{c} \right)}
x=2πn−asin⁡(2c)+πx = 2 \pi n - \operatorname{asin}{\left(\frac{2}{c} \right)} + \pi
O
x=2πn+asin⁡(2c)x = 2 \pi n + \operatorname{asin}{\left(\frac{2}{c} \right)}
x=2πn−asin⁡(2c)+πx = 2 \pi n - \operatorname{asin}{\left(\frac{2}{c} \right)} + \pi
, donde n es cualquier número entero
Gráfica
Respuesta rápida [src] 
            /    /2\\       /    /2\\
x1 = pi - re|asin|-|| - I*im|asin|-||
            \    \c//       \    \c//
x1=−re⁡(asin⁡(2c))−iim⁡(asin⁡(2c))+πx_{1} = - \operatorname{re}{\left(\operatorname{asin}{\left(\frac{2}{c} \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{2}{c} \right)}\right)} + \pi 
         /    /2\\     /    /2\\
x2 = I*im|asin|-|| + re|asin|-||
         \    \c//     \    \c//
x2=re⁡(asin⁡(2c))+iim⁡(asin⁡(2c))x_{2} = \operatorname{re}{\left(\operatorname{asin}{\left(\frac{2}{c} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{2}{c} \right)}\right)} 
x2 = re(asin(2/c)) + i*im(asin(2/c))
Suma y producto de raíces [src] 
suma
       /    /2\\       /    /2\\       /    /2\\     /    /2\\
pi - re|asin|-|| - I*im|asin|-|| + I*im|asin|-|| + re|asin|-||
       \    \c//       \    \c//       \    \c//     \    \c//
(re⁡(asin⁡(2c))+iim⁡(asin⁡(2c)))+(−re⁡(asin⁡(2c))−iim⁡(asin⁡(2c))+π)\left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{2}{c} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{2}{c} \right)}\right)}\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(\frac{2}{c} \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{2}{c} \right)}\right)} + \pi\right) 
=
pi
π\pi 
producto
/       /    /2\\       /    /2\\\ /    /    /2\\     /    /2\\\
|pi - re|asin|-|| - I*im|asin|-|||*|I*im|asin|-|| + re|asin|-|||
\       \    \c//       \    \c/// \    \    \c//     \    \c///
(re⁡(asin⁡(2c))+iim⁡(asin⁡(2c)))(−re⁡(asin⁡(2c))−iim⁡(asin⁡(2c))+π)\left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{2}{c} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{2}{c} \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{asin}{\left(\frac{2}{c} \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{2}{c} \right)}\right)} + \pi\right) 
=
 /    /    /2\\     /    /2\\\ /          /    /2\\     /    /2\\\
-|I*im|asin|-|| + re|asin|-|||*|-pi + I*im|asin|-|| + re|asin|-|||
 \    \    \c//     \    \c/// \          \    \c//     \    \c///
−(re⁡(asin⁡(2c))+iim⁡(asin⁡(2c)))(re⁡(asin⁡(2c))+iim⁡(asin⁡(2c))−π)- \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{2}{c} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{2}{c} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{2}{c} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{2}{c} \right)}\right)} - \pi\right) 
-(i*im(asin(2/c)) + re(asin(2/c)))*(-pi + i*im(asin(2/c)) + re(asin(2/c)))
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