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(cos(t)+2)*3*k-2*sin(t)=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
(cos(t) + 2)*3*k - 2*sin(t) = 0
k3(cos⁡(t)+2)−2sin⁡(t)=0k 3 \left(\cos{\left(t \right)} + 2\right) - 2 \sin{\left(t \right)} = 0
Simplificar
Gráfica
Suma y producto de raíces [src] 
suma
      /    /        ___________\\         /    /        ___________\\       /    /       ___________\\         /    /       ___________\\
      |    |       /         2 ||         |    |       /         2 ||       |    |      /         2 ||         |    |      /         2 ||
      |    |-2 + \/  4 - 27*k  ||         |    |-2 + \/  4 - 27*k  ||       |    |2 + \/  4 - 27*k  ||         |    |2 + \/  4 - 27*k  ||
- 2*re|atan|-------------------|| - 2*I*im|atan|-------------------|| + 2*re|atan|------------------|| + 2*I*im|atan|------------------||
      \    \        3*k        //         \    \        3*k        //       \    \       3*k        //         \    \       3*k        //
(−2re⁡(atan⁡(4−27k2−23k))−2iim⁡(atan⁡(4−27k2−23k)))+(2re⁡(atan⁡(4−27k2+23k))+2iim⁡(atan⁡(4−27k2+23k)))\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} - 2}{3 k} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} - 2}{3 k} \right)}\right)}\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} + 2}{3 k} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} + 2}{3 k} \right)}\right)}\right) 
=
      /    /        ___________\\       /    /       ___________\\         /    /        ___________\\         /    /       ___________\\
      |    |       /         2 ||       |    |      /         2 ||         |    |       /         2 ||         |    |      /         2 ||
      |    |-2 + \/  4 - 27*k  ||       |    |2 + \/  4 - 27*k  ||         |    |-2 + \/  4 - 27*k  ||         |    |2 + \/  4 - 27*k  ||
- 2*re|atan|-------------------|| + 2*re|atan|------------------|| - 2*I*im|atan|-------------------|| + 2*I*im|atan|------------------||
      \    \        3*k        //       \    \       3*k        //         \    \        3*k        //         \    \       3*k        //
−2re⁡(atan⁡(4−27k2−23k))+2re⁡(atan⁡(4−27k2+23k))−2iim⁡(atan⁡(4−27k2−23k))+2iim⁡(atan⁡(4−27k2+23k))- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} - 2}{3 k} \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} + 2}{3 k} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} - 2}{3 k} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} + 2}{3 k} \right)}\right)} 
producto
/      /    /        ___________\\         /    /        ___________\\\ /    /    /       ___________\\         /    /       ___________\\\
|      |    |       /         2 ||         |    |       /         2 ||| |    |    |      /         2 ||         |    |      /         2 |||
|      |    |-2 + \/  4 - 27*k  ||         |    |-2 + \/  4 - 27*k  ||| |    |    |2 + \/  4 - 27*k  ||         |    |2 + \/  4 - 27*k  |||
|- 2*re|atan|-------------------|| - 2*I*im|atan|-------------------|||*|2*re|atan|------------------|| + 2*I*im|atan|------------------|||
\      \    \        3*k        //         \    \        3*k        /// \    \    \       3*k        //         \    \       3*k        ///
(−2re⁡(atan⁡(4−27k2−23k))−2iim⁡(atan⁡(4−27k2−23k)))(2re⁡(atan⁡(4−27k2+23k))+2iim⁡(atan⁡(4−27k2+23k)))\left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} - 2}{3 k} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} - 2}{3 k} \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} + 2}{3 k} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} + 2}{3 k} \right)}\right)}\right) 
=
   /    /    /        ___________\\     /    /        ___________\\\ /    /    /       ___________\\     /    /       ___________\\\
   |    |    |       /         2 ||     |    |       /         2 ||| |    |    |      /         2 ||     |    |      /         2 |||
   |    |    |-2 + \/  4 - 27*k  ||     |    |-2 + \/  4 - 27*k  ||| |    |    |2 + \/  4 - 27*k  ||     |    |2 + \/  4 - 27*k  |||
-4*|I*im|atan|-------------------|| + re|atan|-------------------|||*|I*im|atan|------------------|| + re|atan|------------------|||
   \    \    \        3*k        //     \    \        3*k        /// \    \    \       3*k        //     \    \       3*k        ///
−4(re⁡(atan⁡(4−27k2−23k))+iim⁡(atan⁡(4−27k2−23k)))(re⁡(atan⁡(4−27k2+23k))+iim⁡(atan⁡(4−27k2+23k)))- 4 \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} - 2}{3 k} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} - 2}{3 k} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} + 2}{3 k} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} + 2}{3 k} \right)}\right)}\right) 
-4*(i*im(atan((-2 + sqrt(4 - 27*k^2))/(3*k))) + re(atan((-2 + sqrt(4 - 27*k^2))/(3*k))))*(i*im(atan((2 + sqrt(4 - 27*k^2))/(3*k))) + re(atan((2 + sqrt(4 - 27*k^2))/(3*k))))
Respuesta rápida [src] 
           /    /        ___________\\         /    /        ___________\\
           |    |       /         2 ||         |    |       /         2 ||
           |    |-2 + \/  4 - 27*k  ||         |    |-2 + \/  4 - 27*k  ||
t1 = - 2*re|atan|-------------------|| - 2*I*im|atan|-------------------||
           \    \        3*k        //         \    \        3*k        //
t1=−2re⁡(atan⁡(4−27k2−23k))−2iim⁡(atan⁡(4−27k2−23k))t_{1} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} - 2}{3 k} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} - 2}{3 k} \right)}\right)} 
         /    /       ___________\\         /    /       ___________\\
         |    |      /         2 ||         |    |      /         2 ||
         |    |2 + \/  4 - 27*k  ||         |    |2 + \/  4 - 27*k  ||
t2 = 2*re|atan|------------------|| + 2*I*im|atan|------------------||
         \    \       3*k        //         \    \       3*k        //
t2=2re⁡(atan⁡(4−27k2+23k))+2iim⁡(atan⁡(4−27k2+23k))t_{2} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} + 2}{3 k} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{\sqrt{4 - 27 k^{2}} + 2}{3 k} \right)}\right)} 
t2 = 2*re(atan((sqrt(4 - 27*k^2) + 2)/(3*k))) + 2*i*im(atan((sqrt(4 - 27*k^2) + 2)/(3*k)))
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