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3^-2/2*cosx-1/2*sinx=1 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
cos(x)   sin(x)    
------ - ------ = 1
  3        2
$$- \frac{\sin{\left(x \right)}}{2} + \frac{\cos{\left(x \right)}}{3} = 1$$
Simplificar
Gráfica
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
      /    /        ____\\         /    /        ____\\         /    /        ____\\         /    /        ____\\
      |    |3   I*\/ 23 ||         |    |3   I*\/ 23 ||         |    |3   I*\/ 23 ||         |    |3   I*\/ 23 ||
- 2*re|atan|- - --------|| - 2*I*im|atan|- - --------|| + - 2*re|atan|- + --------|| - 2*I*im|atan|- + --------||
      \    \8      8    //         \    \8      8    //         \    \8      8    //         \    \8      8    //
$$\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3}{8} + \frac{\sqrt{23} i}{8} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3}{8} + \frac{\sqrt{23} i}{8} \right)}\right)}\right) + \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3}{8} - \frac{\sqrt{23} i}{8} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3}{8} - \frac{\sqrt{23} i}{8} \right)}\right)}\right)$$ 
=
      /    /        ____\\       /    /        ____\\         /    /        ____\\         /    /        ____\\
      |    |3   I*\/ 23 ||       |    |3   I*\/ 23 ||         |    |3   I*\/ 23 ||         |    |3   I*\/ 23 ||
- 2*re|atan|- - --------|| - 2*re|atan|- + --------|| - 2*I*im|atan|- - --------|| - 2*I*im|atan|- + --------||
      \    \8      8    //       \    \8      8    //         \    \8      8    //         \    \8      8    //
$$- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3}{8} - \frac{\sqrt{23} i}{8} \right)}\right)} - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3}{8} + \frac{\sqrt{23} i}{8} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3}{8} + \frac{\sqrt{23} i}{8} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3}{8} - \frac{\sqrt{23} i}{8} \right)}\right)}$$ 
producto
/      /    /        ____\\         /    /        ____\\\ /      /    /        ____\\         /    /        ____\\\
|      |    |3   I*\/ 23 ||         |    |3   I*\/ 23 ||| |      |    |3   I*\/ 23 ||         |    |3   I*\/ 23 |||
|- 2*re|atan|- - --------|| - 2*I*im|atan|- - --------|||*|- 2*re|atan|- + --------|| - 2*I*im|atan|- + --------|||
\      \    \8      8    //         \    \8      8    /// \      \    \8      8    //         \    \8      8    ///
$$\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3}{8} - \frac{\sqrt{23} i}{8} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3}{8} - \frac{\sqrt{23} i}{8} \right)}\right)}\right) \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3}{8} + \frac{\sqrt{23} i}{8} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3}{8} + \frac{\sqrt{23} i}{8} \right)}\right)}\right)$$ 
=
  /    /    /        ____\\     /    /        ____\\\ /    /    /        ____\\     /    /        ____\\\
  |    |    |3   I*\/ 23 ||     |    |3   I*\/ 23 ||| |    |    |3   I*\/ 23 ||     |    |3   I*\/ 23 |||
4*|I*im|atan|- - --------|| + re|atan|- - --------|||*|I*im|atan|- + --------|| + re|atan|- + --------|||
  \    \    \8      8    //     \    \8      8    /// \    \    \8      8    //     \    \8      8    ///
$$4 \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{3}{8} - \frac{\sqrt{23} i}{8} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3}{8} - \frac{\sqrt{23} i}{8} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{3}{8} + \frac{\sqrt{23} i}{8} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3}{8} + \frac{\sqrt{23} i}{8} \right)}\right)}\right)$$ 
4*(i*im(atan(3/8 - i*sqrt(23)/8)) + re(atan(3/8 - i*sqrt(23)/8)))*(i*im(atan(3/8 + i*sqrt(23)/8)) + re(atan(3/8 + i*sqrt(23)/8)))
Respuesta rápida [src] 
           /    /        ____\\         /    /        ____\\
           |    |3   I*\/ 23 ||         |    |3   I*\/ 23 ||
x1 = - 2*re|atan|- - --------|| - 2*I*im|atan|- - --------||
           \    \8      8    //         \    \8      8    //
$$x_{1} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3}{8} - \frac{\sqrt{23} i}{8} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3}{8} - \frac{\sqrt{23} i}{8} \right)}\right)}$$ 
           /    /        ____\\         /    /        ____\\
           |    |3   I*\/ 23 ||         |    |3   I*\/ 23 ||
x2 = - 2*re|atan|- + --------|| - 2*I*im|atan|- + --------||
           \    \8      8    //         \    \8      8    //
$$x_{2} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3}{8} + \frac{\sqrt{23} i}{8} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3}{8} + \frac{\sqrt{23} i}{8} \right)}\right)}$$ 
x2 = -2*re(atan(3/8 + sqrt(23)*i/8)) - 2*i*im(atan(3/8 + sqrt(23)*i/8))
Respuesta numérica [src] 
x1 = -0.982793723247329 + 1.09668541083015*i
x2 = -0.982793723247329 - 1.09668541083015*i
x2 = -0.982793723247329 - 1.09668541083015*i
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