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sin(2*p+x)+cos(3*p/2-x)=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
                  /3*p    \    
sin(2*p + x) + cos|--- - x| = 0
                  \ 2     /
sin⁡(2p+x)+cos⁡(3p2−x)=0\sin{\left(2 p + x \right)} + \cos{\left(\frac{3 p}{2} - x \right)} = 0
Simplificar
Gráfica
Respuesta rápida [src] 
       /            /|     _________          _________|\\      /      _________        \
       |            ||    /   -I*p           /   -I*p  |||      |     /   -I*p          |
       |            ||   /    -----         /    ----- |||      |    /    -----         |
       |log(2)      ||  /       2          /       2   |||      |   /       2           |
x1 = I*|------ - log\|\/    -e       + I*\/    -e      |/| + arg\-\/    -e      *(1 + I)/
       \  2                                              /
x1=i(−log⁡(∣−e−ip2+i−e−ip2∣)+log⁡(2)2)+arg⁡(−−e−ip2(1+i))x_{1} = i \left(- \log{\left(\left|{\sqrt{- e^{- \frac{i p}{2}}} + i \sqrt{- e^{- \frac{i p}{2}}}}\right| \right)} + \frac{\log{\left(2 \right)}}{2}\right) + \arg{\left(- \sqrt{- e^{- \frac{i p}{2}}} \left(1 + i\right) \right)} 
       /            /|     _________          _________|\\      /     _________        \
       |            ||    /   -I*p           /   -I*p  |||      |    /   -I*p          |
       |            ||   /    -----         /    ----- |||      |   /    -----         |
       |log(2)      ||  /       2          /       2   |||      |  /       2           |
x2 = I*|------ - log\|\/    -e       + I*\/    -e      |/| + arg\\/    -e      *(1 + I)/
       \  2                                              /
x2=i(−log⁡(∣−e−ip2+i−e−ip2∣)+log⁡(2)2)+arg⁡(−e−ip2(1+i))x_{2} = i \left(- \log{\left(\left|{\sqrt{- e^{- \frac{i p}{2}}} + i \sqrt{- e^{- \frac{i p}{2}}}}\right| \right)} + \frac{\log{\left(2 \right)}}{2}\right) + \arg{\left(\sqrt{- e^{- \frac{i p}{2}}} \left(1 + i\right) \right)} 
                     /  -2*I*p\
x3 = -2*I*im(p) + arg\-e      /
x3=−2iim⁡(p)+arg⁡(−e−2ip)x_{3} = - 2 i \operatorname{im}{\left(p\right)} + \arg{\left(- e^{- 2 i p} \right)} 
                    /  3*I*p\
                    |  -----|
     3*I*im(p)      |    2  |
x4 = --------- + arg\-e     /
         2
x4=3iim⁡(p)2+arg⁡(−e3ip2)x_{4} = \frac{3 i \operatorname{im}{\left(p\right)}}{2} + \arg{\left(- e^{\frac{3 i p}{2}} \right)} 
x4 = 3*i*im(p)/2 + arg(-exp(3*i*p/2))
Suma y producto de raíces [src] 
suma
  /            /|     _________          _________|\\      /      _________        \     /            /|     _________          _________|\\      /     _________        \                                                        
  |            ||    /   -I*p           /   -I*p  |||      |     /   -I*p          |     |            ||    /   -I*p           /   -I*p  |||      |    /   -I*p          |                                               /  3*I*p\
  |            ||   /    -----         /    ----- |||      |    /    -----         |     |            ||   /    -----         /    ----- |||      |   /    -----         |                                               |  -----|
  |log(2)      ||  /       2          /       2   |||      |   /       2           |     |log(2)      ||  /       2          /       2   |||      |  /       2           |                   /  -2*I*p\   3*I*im(p)      |    2  |
I*|------ - log\|\/    -e       + I*\/    -e      |/| + arg\-\/    -e      *(1 + I)/ + I*|------ - log\|\/    -e       + I*\/    -e      |/| + arg\\/    -e      *(1 + I)/ + -2*I*im(p) + arg\-e      / + --------- + arg\-e     /
  \  2                                              /                                    \  2                                              /                                                                  2
(3iim⁡(p)2+arg⁡(−e3ip2))+((−2iim⁡(p)+arg⁡(−e−2ip))+((i(−log⁡(∣−e−ip2+i−e−ip2∣)+log⁡(2)2)+arg⁡(−−e−ip2(1+i)))+(i(−log⁡(∣−e−ip2+i−e−ip2∣)+log⁡(2)2)+arg⁡(−e−ip2(1+i)))))\left(\frac{3 i \operatorname{im}{\left(p\right)}}{2} + \arg{\left(- e^{\frac{3 i p}{2}} \right)}\right) + \left(\left(- 2 i \operatorname{im}{\left(p\right)} + \arg{\left(- e^{- 2 i p} \right)}\right) + \left(\left(i \left(- \log{\left(\left|{\sqrt{- e^{- \frac{i p}{2}}} + i \sqrt{- e^{- \frac{i p}{2}}}}\right| \right)} + \frac{\log{\left(2 \right)}}{2}\right) + \arg{\left(- \sqrt{- e^{- \frac{i p}{2}}} \left(1 + i\right) \right)}\right) + \left(i \left(- \log{\left(\left|{\sqrt{- e^{- \frac{i p}{2}}} + i \sqrt{- e^{- \frac{i p}{2}}}}\right| \right)} + \frac{\log{\left(2 \right)}}{2}\right) + \arg{\left(\sqrt{- e^{- \frac{i p}{2}}} \left(1 + i\right) \right)}\right)\right)\right) 
=
    /            /|     _________          _________|\\                                               /     _________        \      /      _________        \
    |            ||    /   -I*p           /   -I*p  |||                                /  3*I*p\      |    /   -I*p          |      |     /   -I*p          |
    |            ||   /    -----         /    ----- |||                                |  -----|      |   /    -----         |      |    /    -----         |
    |log(2)      ||  /       2          /       2   |||   I*im(p)      /  -2*I*p\      |    2  |      |  /       2           |      |   /       2           |
2*I*|------ - log\|\/    -e       + I*\/    -e      |/| - ------- + arg\-e      / + arg\-e     / + arg\\/    -e      *(1 + I)/ + arg\-\/    -e      *(1 + I)/
    \  2                                              /      2
2i(−log⁡(∣−e−ip2+i−e−ip2∣)+log⁡(2)2)−iim⁡(p)2+arg⁡(−−e−ip2(1+i))+arg⁡(−e−ip2(1+i))+arg⁡(−e−2ip)+arg⁡(−e3ip2)2 i \left(- \log{\left(\left|{\sqrt{- e^{- \frac{i p}{2}}} + i \sqrt{- e^{- \frac{i p}{2}}}}\right| \right)} + \frac{\log{\left(2 \right)}}{2}\right) - \frac{i \operatorname{im}{\left(p\right)}}{2} + \arg{\left(- \sqrt{- e^{- \frac{i p}{2}}} \left(1 + i\right) \right)} + \arg{\left(\sqrt{- e^{- \frac{i p}{2}}} \left(1 + i\right) \right)} + \arg{\left(- e^{- 2 i p} \right)} + \arg{\left(- e^{\frac{3 i p}{2}} \right)} 
producto
/  /            /|     _________          _________|\\      /      _________        \\ /  /            /|     _________          _________|\\      /     _________        \\                                                        
|  |            ||    /   -I*p           /   -I*p  |||      |     /   -I*p          || |  |            ||    /   -I*p           /   -I*p  |||      |    /   -I*p          ||                              /               /  3*I*p\\
|  |            ||   /    -----         /    ----- |||      |    /    -----         || |  |            ||   /    -----         /    ----- |||      |   /    -----         ||                              |               |  -----||
|  |log(2)      ||  /       2          /       2   |||      |   /       2           || |  |log(2)      ||  /       2          /       2   |||      |  /       2           || /                /  -2*I*p\\ |3*I*im(p)      |    2  ||
|I*|------ - log\|\/    -e       + I*\/    -e      |/| + arg\-\/    -e      *(1 + I)/|*|I*|------ - log\|\/    -e       + I*\/    -e      |/| + arg\\/    -e      *(1 + I)/|*\-2*I*im(p) + arg\-e      //*|--------- + arg\-e     /|
\  \  2                                              /                               / \  \  2                                              /                              /                              \    2                   /
(i(−log⁡(∣−e−ip2+i−e−ip2∣)+log⁡(2)2)+arg⁡(−−e−ip2(1+i)))(i(−log⁡(∣−e−ip2+i−e−ip2∣)+log⁡(2)2)+arg⁡(−e−ip2(1+i)))(−2iim⁡(p)+arg⁡(−e−2ip))(3iim⁡(p)2+arg⁡(−e3ip2))\left(i \left(- \log{\left(\left|{\sqrt{- e^{- \frac{i p}{2}}} + i \sqrt{- e^{- \frac{i p}{2}}}}\right| \right)} + \frac{\log{\left(2 \right)}}{2}\right) + \arg{\left(- \sqrt{- e^{- \frac{i p}{2}}} \left(1 + i\right) \right)}\right) \left(i \left(- \log{\left(\left|{\sqrt{- e^{- \frac{i p}{2}}} + i \sqrt{- e^{- \frac{i p}{2}}}}\right| \right)} + \frac{\log{\left(2 \right)}}{2}\right) + \arg{\left(\sqrt{- e^{- \frac{i p}{2}}} \left(1 + i\right) \right)}\right) \left(- 2 i \operatorname{im}{\left(p\right)} + \arg{\left(- e^{- 2 i p} \right)}\right) \left(\frac{3 i \operatorname{im}{\left(p\right)}}{2} + \arg{\left(- e^{\frac{3 i p}{2}} \right)}\right) 
=
                               /     /     _________        \        /|     _________|\\ /     /      _________        \        /|     _________|\\                              
                               |     |    /   -I*p          |        ||    /   -I*p  ||| |     |     /   -I*p          |        ||    /   -I*p  ||| /     /  3*I*p\            \ 
                               |     |   /    -----         |        ||   /    ----- ||| |     |    /    -----         |        ||   /    ----- ||| |     |  -----|            | 
 /     /  -2*I*p\            \ |     |  /       2           |        ||  /       2   ||| |     |   /       2           |        ||  /       2   ||| |     |    2  |            | 
-\- arg\-e      / + 2*I*im(p)/*\- arg\\/    -e      *(1 + I)/ + I*log\|\/    -e      |//*\- arg\-\/    -e      *(1 + I)/ + I*log\|\/    -e      |//*\2*arg\-e     / + 3*I*im(p)/ 
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                        2
−(ilog⁡(∣−e−ip2∣)−arg⁡(−−e−ip2(1+i)))(ilog⁡(∣−e−ip2∣)−arg⁡(−e−ip2(1+i)))(2iim⁡(p)−arg⁡(−e−2ip))(3iim⁡(p)+2arg⁡(−e3ip2))2- \frac{\left(i \log{\left(\left|{\sqrt{- e^{- \frac{i p}{2}}}}\right| \right)} - \arg{\left(- \sqrt{- e^{- \frac{i p}{2}}} \left(1 + i\right) \right)}\right) \left(i \log{\left(\left|{\sqrt{- e^{- \frac{i p}{2}}}}\right| \right)} - \arg{\left(\sqrt{- e^{- \frac{i p}{2}}} \left(1 + i\right) \right)}\right) \left(2 i \operatorname{im}{\left(p\right)} - \arg{\left(- e^{- 2 i p} \right)}\right) \left(3 i \operatorname{im}{\left(p\right)} + 2 \arg{\left(- e^{\frac{3 i p}{2}} \right)}\right)}{2} 
-(-arg(-exp(-2*i*p)) + 2*i*im(p))*(-arg(sqrt(-exp(-i*p/2))*(1 + i)) + i*log(Abs(sqrt(-exp(-i*p/2)))))*(-arg(-sqrt(-exp(-i*p/2))*(1 + i)) + i*log(Abs(sqrt(-exp(-i*p/2)))))*(2*arg(-exp(3*i*p/2)) + 3*i*im(p))/2
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