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sin(z)-cos(z)=3

sin(z)-cos(z)=3 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
sin(z) - cos(z) = 3
sin⁡(z)−cos⁡(z)=3\sin{\left(z \right)} - \cos{\left(z \right)} = 3
Simplificar
Gráfica
0-80-60-40-2020406080-1001005-5
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
         /    /        ___\\         /    /        ___\\
         |    |1   I*\/ 7 ||         |    |1   I*\/ 7 ||
z1 = 2*re|atan|- - -------|| + 2*I*im|atan|- - -------||
         \    \2      2   //         \    \2      2   //
z1=2re⁡(atan⁡(12−7i2))+2iim⁡(atan⁡(12−7i2))z_{1} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{7} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{7} i}{2} \right)}\right)} 
         /    /        ___\\         /    /        ___\\
         |    |1   I*\/ 7 ||         |    |1   I*\/ 7 ||
z2 = 2*re|atan|- + -------|| + 2*I*im|atan|- + -------||
         \    \2      2   //         \    \2      2   //
z2=2re⁡(atan⁡(12+7i2))+2iim⁡(atan⁡(12+7i2))z_{2} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{7} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{7} i}{2} \right)}\right)} 
z2 = 2*re(atan(1/2 + sqrt(7)*i/2)) + 2*i*im(atan(1/2 + sqrt(7)*i/2))
Suma y producto de raíces [src] 
suma
    /    /        ___\\         /    /        ___\\       /    /        ___\\         /    /        ___\\
    |    |1   I*\/ 7 ||         |    |1   I*\/ 7 ||       |    |1   I*\/ 7 ||         |    |1   I*\/ 7 ||
2*re|atan|- - -------|| + 2*I*im|atan|- - -------|| + 2*re|atan|- + -------|| + 2*I*im|atan|- + -------||
    \    \2      2   //         \    \2      2   //       \    \2      2   //         \    \2      2   //
(2re⁡(atan⁡(12−7i2))+2iim⁡(atan⁡(12−7i2)))+(2re⁡(atan⁡(12+7i2))+2iim⁡(atan⁡(12+7i2)))\left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{7} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{7} i}{2} \right)}\right)}\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{7} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{7} i}{2} \right)}\right)}\right) 
=
    /    /        ___\\       /    /        ___\\         /    /        ___\\         /    /        ___\\
    |    |1   I*\/ 7 ||       |    |1   I*\/ 7 ||         |    |1   I*\/ 7 ||         |    |1   I*\/ 7 ||
2*re|atan|- + -------|| + 2*re|atan|- - -------|| + 2*I*im|atan|- + -------|| + 2*I*im|atan|- - -------||
    \    \2      2   //       \    \2      2   //         \    \2      2   //         \    \2      2   //
2re⁡(atan⁡(12+7i2))+2re⁡(atan⁡(12−7i2))+2iim⁡(atan⁡(12−7i2))+2iim⁡(atan⁡(12+7i2))2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{7} i}{2} \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{7} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{7} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{7} i}{2} \right)}\right)} 
producto
/    /    /        ___\\         /    /        ___\\\ /    /    /        ___\\         /    /        ___\\\
|    |    |1   I*\/ 7 ||         |    |1   I*\/ 7 ||| |    |    |1   I*\/ 7 ||         |    |1   I*\/ 7 |||
|2*re|atan|- - -------|| + 2*I*im|atan|- - -------|||*|2*re|atan|- + -------|| + 2*I*im|atan|- + -------|||
\    \    \2      2   //         \    \2      2   /// \    \    \2      2   //         \    \2      2   ///
(2re⁡(atan⁡(12−7i2))+2iim⁡(atan⁡(12−7i2)))(2re⁡(atan⁡(12+7i2))+2iim⁡(atan⁡(12+7i2)))\left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{7} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{7} i}{2} \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{7} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{7} i}{2} \right)}\right)}\right) 
=
  /    /    /        ___\\     /    /        ___\\\ /    /    /        ___\\     /    /        ___\\\
  |    |    |1   I*\/ 7 ||     |    |1   I*\/ 7 ||| |    |    |1   I*\/ 7 ||     |    |1   I*\/ 7 |||
4*|I*im|atan|- + -------|| + re|atan|- + -------|||*|I*im|atan|- - -------|| + re|atan|- - -------|||
  \    \    \2      2   //     \    \2      2   /// \    \    \2      2   //     \    \2      2   ///
4(re⁡(atan⁡(12−7i2))+iim⁡(atan⁡(12−7i2)))(re⁡(atan⁡(12+7i2))+iim⁡(atan⁡(12+7i2)))4 \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{7} i}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{7} i}{2} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{7} i}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{7} i}{2} \right)}\right)}\right) 
4*(i*im(atan(1/2 + i*sqrt(7)/2)) + re(atan(1/2 + i*sqrt(7)/2)))*(i*im(atan(1/2 - i*sqrt(7)/2)) + re(atan(1/2 - i*sqrt(7)/2)))
Respuesta numérica [src] 
z1 = 2.35619449019234 - 1.38432969165679*i
z2 = 2.35619449019234 + 1.38432969165679*i
z2 = 2.35619449019234 + 1.38432969165679*i
Gráfico
sin(z)-cos(z)=3 la ecuación
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