sin(x)=a la ecuación
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Solución
Solución detallada
Tenemos la ecuación
$$\sin{\left(x \right)} = a$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = 2 \pi n + \operatorname{asin}{\left(a \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(a \right)} + \pi$$
O
$$x = 2 \pi n + \operatorname{asin}{\left(a \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(a \right)} + \pi$$
, donde n es cualquier número entero
Suma y producto de raíces
[src]
pi - re(asin(a)) - I*im(asin(a)) + I*im(asin(a)) + re(asin(a))
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(a \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(a \right)}\right)}\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(a \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(a \right)}\right)} + \pi\right)$$
$$\pi$$
(pi - re(asin(a)) - I*im(asin(a)))*(I*im(asin(a)) + re(asin(a)))
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(a \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(a \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{asin}{\left(a \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(a \right)}\right)} + \pi\right)$$
-(I*im(asin(a)) + re(asin(a)))*(-pi + I*im(asin(a)) + re(asin(a)))
$$- \left(\operatorname{re}{\left(\operatorname{asin}{\left(a \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(a \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(a \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(a \right)}\right)} - \pi\right)$$
-(i*im(asin(a)) + re(asin(a)))*(-pi + i*im(asin(a)) + re(asin(a)))
x1 = pi - re(asin(a)) - I*im(asin(a))
$$x_{1} = - \operatorname{re}{\left(\operatorname{asin}{\left(a \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(a \right)}\right)} + \pi$$
x2 = I*im(asin(a)) + re(asin(a))
$$x_{2} = \operatorname{re}{\left(\operatorname{asin}{\left(a \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(a \right)}\right)}$$
x2 = re(asin(a)) + i*im(asin(a))