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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
−3x2+sin⁡(x+y)=110- \frac{3 x}{2} + \sin{\left(x + y \right)} = \frac{1}{10}
Simplificar
Solución detallada
Tenemos la ecuación
−3x2+sin⁡(x+y)=110- \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=2πn+asin⁡(3x2+110)x + y = 2 \pi n + \operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}
x+y=2πn−asin⁡(3x2+110)+πx + y = 2 \pi n - \operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)} + \pi
O
x+y=2πn+asin⁡(3x2+110)x + y = 2 \pi n + \operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}
x+y=2πn−asin⁡(3x2+110)+πx + y = 2 \pi n - \operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)} + \pi
, donde n es cualquier número entero
Transportemos
xx
al miembro derecho de la ecuación
con el signo opuesto, en total:
y=2πn−x+asin⁡(3x2+110)y = 2 \pi n - x + \operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}
y=2πn−x−asin⁡(3x2+110)+πy = 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 //
y1=i(−im⁡(x)+im⁡(asin⁡(3x2+110)))−re⁡(x)+re⁡(asin⁡(3x2+110))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 ///
y2=i(−im⁡(x)−im⁡(asin⁡(3x2+110)))−re⁡(x)−re⁡(asin⁡(3x2+110))+πy_{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 ///
(i(−im⁡(x)+im⁡(asin⁡(3x2+110)))−re⁡(x)+re⁡(asin⁡(3x2+110)))+(i(−im⁡(x)−im⁡(asin⁡(3x2+110)))−re⁡(x)−re⁡(asin⁡(3x2+110))+π)\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(−im⁡(x)−im⁡(asin⁡(3x2+110)))+i(−im⁡(x)+im⁡(asin⁡(3x2+110)))−2re⁡(x)+πi \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 ////
(i(−im⁡(x)+im⁡(asin⁡(3x2+110)))−re⁡(x)+re⁡(asin⁡(3x2+110)))(i(−im⁡(x)−im⁡(asin⁡(3x2+110)))−re⁡(x)−re⁡(asin⁡(3x2+110))+π)\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 ///
(i(im⁡(x)−im⁡(asin⁡(3x2+110)))+re⁡(x)−re⁡(asin⁡(3x2+110)))(i(im⁡(x)+im⁡(asin⁡(3x2+110)))+re⁡(x)+re⁡(asin⁡(3x2+110))−π)\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)))
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