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sin(x)=a la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
sin(x) = a
sin⁡(x)=a\sin{\left(x \right)} = a
Simplificar
Solución detallada
Tenemos la ecuación
sin⁡(x)=a\sin{\left(x \right)} = a
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
x=2πn+asin⁡(a)x = 2 \pi n + \operatorname{asin}{\left(a \right)}
x=2πn−asin⁡(a)+πx = 2 \pi n - \operatorname{asin}{\left(a \right)} + \pi
O
x=2πn+asin⁡(a)x = 2 \pi n + \operatorname{asin}{\left(a \right)}
x=2πn−asin⁡(a)+πx = 2 \pi n - \operatorname{asin}{\left(a \right)} + \pi
, donde n es cualquier número entero
Gráfica
Suma y producto de raíces [src] 
suma
pi - re(asin(a)) - I*im(asin(a)) + I*im(asin(a)) + re(asin(a))
(re⁡(asin⁡(a))+iim⁡(asin⁡(a)))+(−re⁡(asin⁡(a))−iim⁡(asin⁡(a))+π)\left(\operatorname{re}{\left(\operatorname{asin}{\left(a \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(a \right)}\right)}\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(a \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(a \right)}\right)} + \pi\right) 
=
pi
π\pi 
producto
(pi - re(asin(a)) - I*im(asin(a)))*(I*im(asin(a)) + re(asin(a)))
(re⁡(asin⁡(a))+iim⁡(asin⁡(a)))(−re⁡(asin⁡(a))−iim⁡(asin⁡(a))+π)\left(\operatorname{re}{\left(\operatorname{asin}{\left(a \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(a \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{asin}{\left(a \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(a \right)}\right)} + \pi\right) 
=
-(I*im(asin(a)) + re(asin(a)))*(-pi + I*im(asin(a)) + re(asin(a)))
−(re⁡(asin⁡(a))+iim⁡(asin⁡(a)))(re⁡(asin⁡(a))+iim⁡(asin⁡(a))−π)- \left(\operatorname{re}{\left(\operatorname{asin}{\left(a \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(a \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(a \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(a \right)}\right)} - \pi\right) 
-(i*im(asin(a)) + re(asin(a)))*(-pi + i*im(asin(a)) + re(asin(a)))
Respuesta rápida [src] 
x1 = pi - re(asin(a)) - I*im(asin(a))
x1=−re⁡(asin⁡(a))−iim⁡(asin⁡(a))+πx_{1} = - \operatorname{re}{\left(\operatorname{asin}{\left(a \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(a \right)}\right)} + \pi 
x2 = I*im(asin(a)) + re(asin(a))
x2=re⁡(asin⁡(a))+iim⁡(asin⁡(a))x_{2} = \operatorname{re}{\left(\operatorname{asin}{\left(a \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(a \right)}\right)} 
x2 = re(asin(a)) + i*im(asin(a))
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