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cos(2A)*cos(A)+sin(2A)*sin(A) la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
cos(2*a)*cos(a) + sin(2*a)*sin(a) = 0
$$\sin{\left(a \right)} \sin{\left(2 a \right)} + \cos{\left(a \right)} \cos{\left(2 a \right)} = 0$$
Gráfica
Respuesta rápida [src]
     -pi 
a1 = ----
      2  
$$a_{1} = - \frac{\pi}{2}$$
     pi
a2 = --
     2 
$$a_{2} = \frac{\pi}{2}$$
a2 = pi/2
Suma y producto de raíces [src]
suma
  pi   pi
- -- + --
  2    2 
$$- \frac{\pi}{2} + \frac{\pi}{2}$$
=
0
$$0$$
producto
-pi  pi
----*--
 2   2 
$$- \frac{\pi}{2} \frac{\pi}{2}$$
=
   2 
-pi  
-----
  4  
$$- \frac{\pi^{2}}{4}$$
-pi^2/4
Respuesta numérica [src]
a1 = 48.6946861306418
a2 = 54.9778714378214
a3 = -98.9601685880785
a4 = 67.5442420521806
a5 = 76.9690200129499
a6 = 36.1283155162826
a7 = -3454.18112262198
a8 = 58.1194640914112
a9 = 14.1371669411541
a10 = -29.845130209103
a11 = 61.261056745001
a12 = -36.1283155162826
a13 = -4.71238898038469
a14 = -39.2699081698724
a15 = 1.5707963267949
a16 = -14.1371669411541
a17 = -64.4026493985908
a18 = -67.5442420521806
a19 = 92.6769832808989
a20 = -51.8362787842316
a21 = -86.3937979737193
a22 = 42.4115008234622
a23 = -17.2787595947439
a24 = -45.553093477052
a25 = -89.5353906273091
a26 = -1.5707963267949
a27 = 39.2699081698724
a28 = 23.5619449019235
a29 = 7.85398163397448
a30 = -58.1194640914112
a31 = -61.261056745001
a32 = -73.8274273593601
a33 = 73.8274273593601
a34 = 29.845130209103
a35 = 4.71238898038469
a36 = 86.3937979737193
a37 = 64.4026493985908
a38 = 89.5353906273091
a39 = -20.4203522483337
a40 = -387.986692718339
a41 = -26.7035375555132
a42 = 98.9601685880785
a43 = 51.8362787842316
a44 = 83.2522053201295
a45 = -48.6946861306418
a46 = -54.9778714378214
a47 = 70.6858347057703
a48 = -95.8185759344887
a49 = 26.7035375555132
a50 = 80.1106126665397
a51 = -23.5619449019235
a52 = -7.85398163397448
a53 = -83.2522053201295
a54 = -76.9690200129499
a55 = -42.4115008234622
a56 = -32.9867228626928
a57 = 17.2787595947439
a58 = 32.9867228626928
a59 = 20.4203522483337
a60 = -70.6858347057703
a61 = -10.9955742875643
a62 = -92.6769832808989
a63 = 45.553093477052
a64 = 10.9955742875643
a65 = -80.1106126665397
a66 = 95.8185759344887
a67 = -2266.65909956504
a67 = -2266.65909956504