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sqrt99×sinx-49cosx=51 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
  ____                        
\/ 99 *sin(x) - 49*cos(x) = 51
99sin⁡(x)−49cos⁡(x)=51\sqrt{99} \sin{\left(x \right)} - 49 \cos{\left(x \right)} = 51
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Gráfica
0-80-60-40-2020406080-100100-100100
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
         /    /    ____       _____\\         /    /    ____       _____\\
         |    |3*\/ 11    I*\/ 101 ||         |    |3*\/ 11    I*\/ 101 ||
x1 = 2*re|atan|-------- - ---------|| + 2*I*im|atan|-------- - ---------||
         \    \   2           2    //         \    \   2           2    //
x1=2re⁡(atan⁡(3112−101i2))+2iim⁡(atan⁡(3112−101i2))x_{1} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} - \frac{\sqrt{101} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} - \frac{\sqrt{101} i}{2} \right)}\right)} 
         /    /    ____       _____\\         /    /    ____       _____\\
         |    |3*\/ 11    I*\/ 101 ||         |    |3*\/ 11    I*\/ 101 ||
x2 = 2*re|atan|-------- + ---------|| + 2*I*im|atan|-------- + ---------||
         \    \   2           2    //         \    \   2           2    //
x2=2re⁡(atan⁡(3112+101i2))+2iim⁡(atan⁡(3112+101i2))x_{2} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} + \frac{\sqrt{101} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} + \frac{\sqrt{101} i}{2} \right)}\right)} 
x2 = 2*re(atan(3*sqrt(11)/2 + sqrt(101)*i/2)) + 2*i*im(atan(3*sqrt(11)/2 + sqrt(101)*i/2))
Suma y producto de raíces [src] 
suma
    /    /    ____       _____\\         /    /    ____       _____\\       /    /    ____       _____\\         /    /    ____       _____\\
    |    |3*\/ 11    I*\/ 101 ||         |    |3*\/ 11    I*\/ 101 ||       |    |3*\/ 11    I*\/ 101 ||         |    |3*\/ 11    I*\/ 101 ||
2*re|atan|-------- - ---------|| + 2*I*im|atan|-------- - ---------|| + 2*re|atan|-------- + ---------|| + 2*I*im|atan|-------- + ---------||
    \    \   2           2    //         \    \   2           2    //       \    \   2           2    //         \    \   2           2    //
(2re⁡(atan⁡(3112−101i2))+2iim⁡(atan⁡(3112−101i2)))+(2re⁡(atan⁡(3112+101i2))+2iim⁡(atan⁡(3112+101i2)))\left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} - \frac{\sqrt{101} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} - \frac{\sqrt{101} i}{2} \right)}\right)}\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} + \frac{\sqrt{101} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} + \frac{\sqrt{101} i}{2} \right)}\right)}\right) 
=
    /    /    ____       _____\\       /    /    ____       _____\\         /    /    ____       _____\\         /    /    ____       _____\\
    |    |3*\/ 11    I*\/ 101 ||       |    |3*\/ 11    I*\/ 101 ||         |    |3*\/ 11    I*\/ 101 ||         |    |3*\/ 11    I*\/ 101 ||
2*re|atan|-------- + ---------|| + 2*re|atan|-------- - ---------|| + 2*I*im|atan|-------- + ---------|| + 2*I*im|atan|-------- - ---------||
    \    \   2           2    //       \    \   2           2    //         \    \   2           2    //         \    \   2           2    //
2re⁡(atan⁡(3112+101i2))+2re⁡(atan⁡(3112−101i2))+2iim⁡(atan⁡(3112−101i2))+2iim⁡(atan⁡(3112+101i2))2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} + \frac{\sqrt{101} i}{2} \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} - \frac{\sqrt{101} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} - \frac{\sqrt{101} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} + \frac{\sqrt{101} i}{2} \right)}\right)} 
producto
/    /    /    ____       _____\\         /    /    ____       _____\\\ /    /    /    ____       _____\\         /    /    ____       _____\\\
|    |    |3*\/ 11    I*\/ 101 ||         |    |3*\/ 11    I*\/ 101 ||| |    |    |3*\/ 11    I*\/ 101 ||         |    |3*\/ 11    I*\/ 101 |||
|2*re|atan|-------- - ---------|| + 2*I*im|atan|-------- - ---------|||*|2*re|atan|-------- + ---------|| + 2*I*im|atan|-------- + ---------|||
\    \    \   2           2    //         \    \   2           2    /// \    \    \   2           2    //         \    \   2           2    ///
(2re⁡(atan⁡(3112−101i2))+2iim⁡(atan⁡(3112−101i2)))(2re⁡(atan⁡(3112+101i2))+2iim⁡(atan⁡(3112+101i2)))\left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} - \frac{\sqrt{101} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} - \frac{\sqrt{101} i}{2} \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} + \frac{\sqrt{101} i}{2} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} + \frac{\sqrt{101} i}{2} \right)}\right)}\right) 
=
  /    /    /    ____       _____\\     /    /    ____       _____\\\ /    /    /    ____       _____\\     /    /    ____       _____\\\
  |    |    |3*\/ 11    I*\/ 101 ||     |    |3*\/ 11    I*\/ 101 ||| |    |    |3*\/ 11    I*\/ 101 ||     |    |3*\/ 11    I*\/ 101 |||
4*|I*im|atan|-------- + ---------|| + re|atan|-------- + ---------|||*|I*im|atan|-------- - ---------|| + re|atan|-------- - ---------|||
  \    \    \   2           2    //     \    \   2           2    /// \    \    \   2           2    //     \    \   2           2    ///
4(re⁡(atan⁡(3112−101i2))+iim⁡(atan⁡(3112−101i2)))(re⁡(atan⁡(3112+101i2))+iim⁡(atan⁡(3112+101i2)))4 \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} - \frac{\sqrt{101} i}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} - \frac{\sqrt{101} i}{2} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} + \frac{\sqrt{101} i}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3 \sqrt{11}}{2} + \frac{\sqrt{101} i}{2} \right)}\right)}\right) 
4*(i*im(atan(3*sqrt(11)/2 + i*sqrt(101)/2)) + re(atan(3*sqrt(11)/2 + i*sqrt(101)/2)))*(i*im(atan(3*sqrt(11)/2 - i*sqrt(101)/2)) + re(atan(3*sqrt(11)/2 - i*sqrt(101)/2)))
Respuesta numérica [src] 
x1 = 2.94125781126667 - 0.199668157798415*i
x2 = 2.94125781126667 + 0.199668157798415*i
x2 = 2.94125781126667 + 0.199668157798415*i
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