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sin(x)+cos(y)=sqrt(2) la ecuación

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Solución numérica:

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Solución

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