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cos(x)+sin(x)=5 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
cos(x) + sin(x) = 5
$$\sin{\left(x \right)} + \cos{\left(x \right)} = 5$$
Simplificar
Gráfica
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
         /    /        ____\\         /    /        ____\\
         |    |1   I*\/ 23 ||         |    |1   I*\/ 23 ||
x1 = 2*re|atan|- - --------|| + 2*I*im|atan|- - --------||
         \    \6      6    //         \    \6      6    //
$$x_{1} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{6} - \frac{\sqrt{23} i}{6} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{6} - \frac{\sqrt{23} i}{6} \right)}\right)}$$ 
         /    /        ____\\         /    /        ____\\
         |    |1   I*\/ 23 ||         |    |1   I*\/ 23 ||
x2 = 2*re|atan|- + --------|| + 2*I*im|atan|- + --------||
         \    \6      6    //         \    \6      6    //
$$x_{2} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{6} + \frac{\sqrt{23} i}{6} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{6} + \frac{\sqrt{23} i}{6} \right)}\right)}$$ 
x2 = 2*re(atan(1/6 + sqrt(23)*i/6)) + 2*i*im(atan(1/6 + sqrt(23)*i/6))
Suma y producto de raíces [src] 
suma
    /    /        ____\\         /    /        ____\\       /    /        ____\\         /    /        ____\\
    |    |1   I*\/ 23 ||         |    |1   I*\/ 23 ||       |    |1   I*\/ 23 ||         |    |1   I*\/ 23 ||
2*re|atan|- - --------|| + 2*I*im|atan|- - --------|| + 2*re|atan|- + --------|| + 2*I*im|atan|- + --------||
    \    \6      6    //         \    \6      6    //       \    \6      6    //         \    \6      6    //
$$\left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{6} - \frac{\sqrt{23} i}{6} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{6} - \frac{\sqrt{23} i}{6} \right)}\right)}\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{6} + \frac{\sqrt{23} i}{6} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{6} + \frac{\sqrt{23} i}{6} \right)}\right)}\right)$$ 
=
    /    /        ____\\       /    /        ____\\         /    /        ____\\         /    /        ____\\
    |    |1   I*\/ 23 ||       |    |1   I*\/ 23 ||         |    |1   I*\/ 23 ||         |    |1   I*\/ 23 ||
2*re|atan|- - --------|| + 2*re|atan|- + --------|| + 2*I*im|atan|- - --------|| + 2*I*im|atan|- + --------||
    \    \6      6    //       \    \6      6    //         \    \6      6    //         \    \6      6    //
$$2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{6} - \frac{\sqrt{23} i}{6} \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{6} + \frac{\sqrt{23} i}{6} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{6} - \frac{\sqrt{23} i}{6} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{6} + \frac{\sqrt{23} i}{6} \right)}\right)}$$ 
producto
/    /    /        ____\\         /    /        ____\\\ /    /    /        ____\\         /    /        ____\\\
|    |    |1   I*\/ 23 ||         |    |1   I*\/ 23 ||| |    |    |1   I*\/ 23 ||         |    |1   I*\/ 23 |||
|2*re|atan|- - --------|| + 2*I*im|atan|- - --------|||*|2*re|atan|- + --------|| + 2*I*im|atan|- + --------|||
\    \    \6      6    //         \    \6      6    /// \    \    \6      6    //         \    \6      6    ///
$$\left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{6} - \frac{\sqrt{23} i}{6} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{6} - \frac{\sqrt{23} i}{6} \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{6} + \frac{\sqrt{23} i}{6} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{6} + \frac{\sqrt{23} i}{6} \right)}\right)}\right)$$ 
=
  /    /    /        ____\\     /    /        ____\\\ /    /    /        ____\\     /    /        ____\\\
  |    |    |1   I*\/ 23 ||     |    |1   I*\/ 23 ||| |    |    |1   I*\/ 23 ||     |    |1   I*\/ 23 |||
4*|I*im|atan|- - --------|| + re|atan|- - --------|||*|I*im|atan|- + --------|| + re|atan|- + --------|||
  \    \    \6      6    //     \    \6      6    /// \    \    \6      6    //     \    \6      6    ///
$$4 \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{6} - \frac{\sqrt{23} i}{6} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{6} - \frac{\sqrt{23} i}{6} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{6} + \frac{\sqrt{23} i}{6} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{6} + \frac{\sqrt{23} i}{6} \right)}\right)}\right)$$ 
4*(i*im(atan(1/6 - i*sqrt(23)/6)) + re(atan(1/6 - i*sqrt(23)/6)))*(i*im(atan(1/6 + i*sqrt(23)/6)) + re(atan(1/6 + i*sqrt(23)/6)))
Respuesta numérica [src] 
x1 = 0.785398163397448 - 1.93538335014355*i
x2 = 0.785398163397448 + 1.93538335014355*i
x2 = 0.785398163397448 + 1.93538335014355*i
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