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2cos^3(x)-2sin^2(x)=-1 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
     3           2        
2*cos (x) - 2*sin (x) = -1
−2sin⁡2(x)+2cos⁡3(x)=−1- 2 \sin^{2}{\left(x \right)} + 2 \cos^{3}{\left(x \right)} = -1
Simplificar
Gráfica
0-80-60-40-2020406080-1001005-5
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
           /       / 6    4       2       \\
x1 = 2*atan\CRootOf\x  - x  + 11*x  - 3, 0//
x1=2atan⁡(CRootOf⁡(x6−x4+11x2−3,0))x_{1} = 2 \operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 0\right)} \right)} 
           /       / 6    4       2       \\
x2 = 2*atan\CRootOf\x  - x  + 11*x  - 3, 1//
x2=2atan⁡(CRootOf⁡(x6−x4+11x2−3,1))x_{2} = 2 \operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 1\right)} \right)} 
         /    /       / 6    4       2       \\\         /    /       / 6    4       2       \\\
x3 = 2*re\atan\CRootOf\x  - x  + 11*x  - 3, 2/// + 2*I*im\atan\CRootOf\x  - x  + 11*x  - 3, 2///
x3=2re⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,2)))+2iim⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,2)))x_{3} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 2\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 2\right)} \right)}\right)} 
         /    /       / 6    4       2       \\\         /    /       / 6    4       2       \\\
x4 = 2*re\atan\CRootOf\x  - x  + 11*x  - 3, 3/// + 2*I*im\atan\CRootOf\x  - x  + 11*x  - 3, 3///
x4=2re⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,3)))+2iim⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,3)))x_{4} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 3\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 3\right)} \right)}\right)} 
         /    /       / 6    4       2       \\\         /    /       / 6    4       2       \\\
x5 = 2*re\atan\CRootOf\x  - x  + 11*x  - 3, 4/// + 2*I*im\atan\CRootOf\x  - x  + 11*x  - 3, 4///
x5=2re⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,4)))+2iim⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,4)))x_{5} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 4\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 4\right)} \right)}\right)} 
         /    /       / 6    4       2       \\\         /    /       / 6    4       2       \\\
x6 = 2*re\atan\CRootOf\x  - x  + 11*x  - 3, 5/// + 2*I*im\atan\CRootOf\x  - x  + 11*x  - 3, 5///
x6=2re⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,5)))+2iim⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,5)))x_{6} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 5\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 5\right)} \right)}\right)} 
Eq(x6, 2*re(atan(CRootOf(x^6 - x^4 + 11*x^2 - 3, 5))) + 2*i*im(atan(CRootOf(x^6 - x^4 + 11*x^2 - 3, 5))))
Suma y producto de raíces [src] 
suma
      /       / 6    4       2       \\         /       / 6    4       2       \\       /    /       / 6    4       2       \\\         /    /       / 6    4       2       \\\       /    /       / 6    4       2       \\\         /    /       / 6    4       2       \\\       /    /       / 6    4       2       \\\         /    /       / 6    4       2       \\\       /    /       / 6    4       2       \\\         /    /       / 6    4       2       \\\
2*atan\CRootOf\x  - x  + 11*x  - 3, 0// + 2*atan\CRootOf\x  - x  + 11*x  - 3, 1// + 2*re\atan\CRootOf\x  - x  + 11*x  - 3, 2/// + 2*I*im\atan\CRootOf\x  - x  + 11*x  - 3, 2/// + 2*re\atan\CRootOf\x  - x  + 11*x  - 3, 3/// + 2*I*im\atan\CRootOf\x  - x  + 11*x  - 3, 3/// + 2*re\atan\CRootOf\x  - x  + 11*x  - 3, 4/// + 2*I*im\atan\CRootOf\x  - x  + 11*x  - 3, 4/// + 2*re\atan\CRootOf\x  - x  + 11*x  - 3, 5/// + 2*I*im\atan\CRootOf\x  - x  + 11*x  - 3, 5///
((((2atan⁡(CRootOf⁡(x6−x4+11x2−3,0))+2atan⁡(CRootOf⁡(x6−x4+11x2−3,1)))+(2re⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,2)))+2iim⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,2)))))+(2re⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,3)))+2iim⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,3)))))+(2re⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,4)))+2iim⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,4)))))+(2re⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,5)))+2iim⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,5))))\left(\left(\left(\left(2 \operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 0\right)} \right)} + 2 \operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 1\right)} \right)}\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 2\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 2\right)} \right)}\right)}\right)\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 3\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 3\right)} \right)}\right)}\right)\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 4\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 4\right)} \right)}\right)}\right)\right) + \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 5\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 5\right)} \right)}\right)}\right) 
=
      /       / 6    4       2       \\         /       / 6    4       2       \\       /    /       / 6    4       2       \\\       /    /       / 6    4       2       \\\       /    /       / 6    4       2       \\\       /    /       / 6    4       2       \\\         /    /       / 6    4       2       \\\         /    /       / 6    4       2       \\\         /    /       / 6    4       2       \\\         /    /       / 6    4       2       \\\
2*atan\CRootOf\x  - x  + 11*x  - 3, 0// + 2*atan\CRootOf\x  - x  + 11*x  - 3, 1// + 2*re\atan\CRootOf\x  - x  + 11*x  - 3, 2/// + 2*re\atan\CRootOf\x  - x  + 11*x  - 3, 3/// + 2*re\atan\CRootOf\x  - x  + 11*x  - 3, 4/// + 2*re\atan\CRootOf\x  - x  + 11*x  - 3, 5/// + 2*I*im\atan\CRootOf\x  - x  + 11*x  - 3, 2/// + 2*I*im\atan\CRootOf\x  - x  + 11*x  - 3, 3/// + 2*I*im\atan\CRootOf\x  - x  + 11*x  - 3, 4/// + 2*I*im\atan\CRootOf\x  - x  + 11*x  - 3, 5///
2re⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,2)))+2re⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,3)))+2atan⁡(CRootOf⁡(x6−x4+11x2−3,0))+2atan⁡(CRootOf⁡(x6−x4+11x2−3,1))+2re⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,4)))+2re⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,5)))+2iim⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,2)))+2iim⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,4)))+2iim⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,3)))+2iim⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,5)))2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 2\right)} \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 3\right)} \right)}\right)} + 2 \operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 0\right)} \right)} + 2 \operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 1\right)} \right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 4\right)} \right)}\right)} + 2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 5\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 2\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 4\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 3\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 5\right)} \right)}\right)} 
producto
      /       / 6    4       2       \\       /       / 6    4       2       \\ /    /    /       / 6    4       2       \\\         /    /       / 6    4       2       \\\\ /    /    /       / 6    4       2       \\\         /    /       / 6    4       2       \\\\ /    /    /       / 6    4       2       \\\         /    /       / 6    4       2       \\\\ /    /    /       / 6    4       2       \\\         /    /       / 6    4       2       \\\\
2*atan\CRootOf\x  - x  + 11*x  - 3, 0//*2*atan\CRootOf\x  - x  + 11*x  - 3, 1//*\2*re\atan\CRootOf\x  - x  + 11*x  - 3, 2/// + 2*I*im\atan\CRootOf\x  - x  + 11*x  - 3, 2////*\2*re\atan\CRootOf\x  - x  + 11*x  - 3, 3/// + 2*I*im\atan\CRootOf\x  - x  + 11*x  - 3, 3////*\2*re\atan\CRootOf\x  - x  + 11*x  - 3, 4/// + 2*I*im\atan\CRootOf\x  - x  + 11*x  - 3, 4////*\2*re\atan\CRootOf\x  - x  + 11*x  - 3, 5/// + 2*I*im\atan\CRootOf\x  - x  + 11*x  - 3, 5////
2atan⁡(CRootOf⁡(x6−x4+11x2−3,0))2atan⁡(CRootOf⁡(x6−x4+11x2−3,1))(2re⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,2)))+2iim⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,2))))(2re⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,3)))+2iim⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,3))))(2re⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,4)))+2iim⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,4))))(2re⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,5)))+2iim⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,5))))2 \operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 0\right)} \right)} 2 \operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 1\right)} \right)} \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 2\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 2\right)} \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 3\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 3\right)} \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 4\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 4\right)} \right)}\right)}\right) \left(2 \operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 5\right)} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 5\right)} \right)}\right)}\right) 
=
   /    /    /       / 6    4       2       \\\     /    /       / 6    4       2       \\\\ /    /    /       / 6    4       2       \\\     /    /       / 6    4       2       \\\\ /    /    /       / 6    4       2       \\\     /    /       / 6    4       2       \\\\ /    /    /       / 6    4       2       \\\     /    /       / 6    4       2       \\\\     /       / 6    4       2       \\     /       / 6    4       2       \\
64*\I*im\atan\CRootOf\x  - x  + 11*x  - 3, 2/// + re\atan\CRootOf\x  - x  + 11*x  - 3, 2////*\I*im\atan\CRootOf\x  - x  + 11*x  - 3, 3/// + re\atan\CRootOf\x  - x  + 11*x  - 3, 3////*\I*im\atan\CRootOf\x  - x  + 11*x  - 3, 4/// + re\atan\CRootOf\x  - x  + 11*x  - 3, 4////*\I*im\atan\CRootOf\x  - x  + 11*x  - 3, 5/// + re\atan\CRootOf\x  - x  + 11*x  - 3, 5////*atan\CRootOf\x  - x  + 11*x  - 3, 0//*atan\CRootOf\x  - x  + 11*x  - 3, 1//
64(re⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,2)))+iim⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,2))))(re⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,3)))+iim⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,3))))(re⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,4)))+iim⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,4))))(re⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,5)))+iim⁡(atan⁡(CRootOf⁡(x6−x4+11x2−3,5))))atan⁡(CRootOf⁡(x6−x4+11x2−3,0))atan⁡(CRootOf⁡(x6−x4+11x2−3,1))64 \left(\operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 2\right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 2\right)} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 3\right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 3\right)} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 4\right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 4\right)} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 5\right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 5\right)} \right)}\right)}\right) \operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 0\right)} \right)} \operatorname{atan}{\left(\operatorname{CRootOf} {\left(x^{6} - x^{4} + 11 x^{2} - 3, 1\right)} \right)} 
64*(i*im(atan(CRootOf(x^6 - x^4 + 11*x^2 - 3, 2))) + re(atan(CRootOf(x^6 - x^4 + 11*x^2 - 3, 2))))*(i*im(atan(CRootOf(x^6 - x^4 + 11*x^2 - 3, 3))) + re(atan(CRootOf(x^6 - x^4 + 11*x^2 - 3, 3))))*(i*im(atan(CRootOf(x^6 - x^4 + 11*x^2 - 3, 4))) + re(atan(CRootOf(x^6 - x^4 + 11*x^2 - 3, 4))))*(i*im(atan(CRootOf(x^6 - x^4 + 11*x^2 - 3, 5))) + re(atan(CRootOf(x^6 - x^4 + 11*x^2 - 3, 5))))*atan(CRootOf(x^6 - x^4 + 11*x^2 - 3, 0))*atan(CRootOf(x^6 - x^4 + 11*x^2 - 3, 1))
Respuesta numérica [src] 
x1 = 26.1028646512358
x2 = 30.4458031133805
x3 = -24.1626178062009
x4 = -19.8196793440562
x5 = -55.5785443420988
x6 = 61.8617296492784
x7 = -99.5608414923559
x8 = -70.0851618014929
x9 = 11.5962471918417
x10 = -32.3860499584154
x11 = 17.8794324990213
x12 = -101.501088337391
x13 = 74.4281002636376
x14 = -5.31306188466215
x15 = 63.8019764943133
x16 = 101.501088337391
x17 = -57.5187911871337
x18 = 38.669235265595
x19 = -13.5364940368766
x20 = -61.8617296492784
x21 = -49.2953590349193
x22 = -68.144914956458
x23 = -17.8794324990213
x24 = 32.3860499584154
x25 = 70.0851618014929
x26 = 68.144914956458
x27 = -220.881609173803
x28 = -26.1028646512358
x29 = 55.5785443420988
x30 = 82.6515324158521
x31 = -63.8019764943133
x32 = 24.1626178062009
x33 = 99.5608414923559
x34 = -76.3683471086725
x35 = -7.25330872969702
x36 = -93.2776561851764
x37 = -11.5962471918417
x38 = -86.9944708779968
x39 = 76.3683471086725
x40 = 7.25330872969702
x41 = 19.8196793440562
x41 = 19.8196793440562
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