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sin(x+y)-1,5*x=0,1 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
             3*x       
sin(x + y) - --- = 1/10
              2        
$$- \frac{3 x}{2} + \sin{\left(x + y \right)} = \frac{1}{10}$$
Solución detallada
Tenemos la ecuación
$$- \frac{3 x}{2} + \sin{\left(x + y \right)} = \frac{1}{10}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x + y = 2 \pi n + \operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}$$
$$x + y = 2 \pi n - \operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)} + \pi$$
O
$$x + y = 2 \pi n + \operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}$$
$$x + y = 2 \pi n - \operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)} + \pi$$
, donde n es cualquier número entero
Transportemos
$$x$$
al miembro derecho de la ecuación
con el signo opuesto, en total:
$$y = 2 \pi n - x + \operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}$$
$$y = 2 \pi n - x - \operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)} + \pi$$
Gráfica
Respuesta rápida [src]
                /           /    /1    3*x\\\     /    /1    3*x\\
y1 = -re(x) + I*|-im(x) + im|asin|-- + ---||| + re|asin|-- + ---||
                \           \    \10    2 ///     \    \10    2 //
$$y_{1} = i \left(- \operatorname{im}{\left(x\right)} + \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}\right)}\right) - \operatorname{re}{\left(x\right)} + \operatorname{re}{\left(\operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}\right)}$$
                    /    /1    3*x\\     /           /    /1    3*x\\\
y2 = pi - re(x) - re|asin|-- + ---|| + I*|-im(x) - im|asin|-- + ---|||
                    \    \10    2 //     \           \    \10    2 ///
$$y_{2} = i \left(- \operatorname{im}{\left(x\right)} - \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}\right)}\right) - \operatorname{re}{\left(x\right)} - \operatorname{re}{\left(\operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}\right)} + \pi$$
y2 = i*(-im(x) - im(asin(3*x/2 + 1/10))) - re(x) - re(asin(3*x/2 + 1/10)) + pi
Suma y producto de raíces [src]
suma
           /           /    /1    3*x\\\     /    /1    3*x\\                  /    /1    3*x\\     /           /    /1    3*x\\\
-re(x) + I*|-im(x) + im|asin|-- + ---||| + re|asin|-- + ---|| + pi - re(x) - re|asin|-- + ---|| + I*|-im(x) - im|asin|-- + ---|||
           \           \    \10    2 ///     \    \10    2 //                  \    \10    2 //     \           \    \10    2 ///
$$\left(i \left(- \operatorname{im}{\left(x\right)} + \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}\right)}\right) - \operatorname{re}{\left(x\right)} + \operatorname{re}{\left(\operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}\right)}\right) + \left(i \left(- \operatorname{im}{\left(x\right)} - \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}\right)}\right) - \operatorname{re}{\left(x\right)} - \operatorname{re}{\left(\operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}\right)} + \pi\right)$$
=
                 /           /    /1    3*x\\\     /           /    /1    3*x\\\
pi - 2*re(x) + I*|-im(x) - im|asin|-- + ---||| + I*|-im(x) + im|asin|-- + ---|||
                 \           \    \10    2 ///     \           \    \10    2 ///
$$i \left(- \operatorname{im}{\left(x\right)} - \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}\right)}\right) + i \left(- \operatorname{im}{\left(x\right)} + \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}\right)}\right) - 2 \operatorname{re}{\left(x\right)} + \pi$$
producto
/           /           /    /1    3*x\\\     /    /1    3*x\\\ /               /    /1    3*x\\     /           /    /1    3*x\\\\
|-re(x) + I*|-im(x) + im|asin|-- + ---||| + re|asin|-- + ---|||*|pi - re(x) - re|asin|-- + ---|| + I*|-im(x) - im|asin|-- + ---||||
\           \           \    \10    2 ///     \    \10    2 /// \               \    \10    2 //     \           \    \10    2 ////
$$\left(i \left(- \operatorname{im}{\left(x\right)} + \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}\right)}\right) - \operatorname{re}{\left(x\right)} + \operatorname{re}{\left(\operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}\right)}\right) \left(i \left(- \operatorname{im}{\left(x\right)} - \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}\right)}\right) - \operatorname{re}{\left(x\right)} - \operatorname{re}{\left(\operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}\right)} + \pi\right)$$
=
/    /    /1    3*x\\     /    /    /1    3*x\\        \        \ /        /          /    /1    3*x\\\             /    /1    3*x\\\
|- re|asin|-- + ---|| + I*|- im|asin|-- + ---|| + im(x)| + re(x)|*|-pi + I*|im(x) + im|asin|-- + ---||| + re(x) + re|asin|-- + ---|||
\    \    \10    2 //     \    \    \10    2 //        /        / \        \          \    \10    2 ///             \    \10    2 ///
$$\left(i \left(\operatorname{im}{\left(x\right)} - \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}\right)}\right) + \operatorname{re}{\left(x\right)} - \operatorname{re}{\left(\operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}\right)}\right) \left(i \left(\operatorname{im}{\left(x\right)} + \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}\right)}\right) + \operatorname{re}{\left(x\right)} + \operatorname{re}{\left(\operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}\right)} - \pi\right)$$
(-re(asin(1/10 + 3*x/2)) + i*(-im(asin(1/10 + 3*x/2)) + im(x)) + re(x))*(-pi + i*(im(x) + im(asin(1/10 + 3*x/2))) + re(x) + re(asin(1/10 + 3*x/2)))