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|sin3t|=1:2 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
|sin(3*t)| = 1/2
$$\left|{\sin{\left(3 t \right)}}\right| = \frac{1}{2}$$
Simplificar
Solución detallada
Tenemos la ecuación
$$\left|{\sin{\left(3 t \right)}}\right| = \frac{1}{2}$$
cambiamos
$$\left|{\sin{\left(3 t \right)}}\right| - \frac{1}{2} = 0$$
$$\left|{\sin{\left(3 t \right)}}\right| - \frac{1}{2} = 0$$
Sustituimos
$$w = \left|{\sin{\left(3 t \right)}}\right|$$
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$w = \frac{1}{2}$$
Obtenemos la respuesta: w = 1/2
hacemos cambio inverso
$$\left|{\sin{\left(3 t \right)}}\right| = w$$
sustituimos w:
Gráfica
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
     -pi 
t1 = ----
      18
$$t_{1} = - \frac{\pi}{18}$$ 
     pi
t2 = --
     18
$$t_{2} = \frac{\pi}{18}$$ 
     5*pi
t3 = ----
      18
$$t_{3} = \frac{5 \pi}{18}$$ 
     7*pi
t4 = ----
      18
$$t_{4} = \frac{7 \pi}{18}$$ 
t4 = 7*pi/18
Suma y producto de raíces [src] 
suma
  pi   pi   5*pi   7*pi
- -- + -- + ---- + ----
  18   18    18     18
$$\left(\left(- \frac{\pi}{18} + \frac{\pi}{18}\right) + \frac{5 \pi}{18}\right) + \frac{7 \pi}{18}$$ 
=
2*pi
----
 3
$$\frac{2 \pi}{3}$$ 
producto
-pi  pi 5*pi 7*pi
----*--*----*----
 18  18  18   18
$$\frac{7 \pi}{18} \frac{5 \pi}{18} \cdot - \frac{\pi}{18} \frac{\pi}{18}$$ 
=
      4
-35*pi 
-------
 104976
$$- \frac{35 \pi^{4}}{104976}$$ 
-35*pi^4/104976
Respuesta numérica [src] 
t1 = 24.2600766027212
t2 = 78.3652834145454
t3 = -86.0447321233204
t4 = -21.8166156499291
t5 = -78.3652834145454
t6 = 6.10865238198015
t7 = 76.2708883121522
t8 = -19.7222205475359
t9 = 54.2797397370236
t10 = 28.0998009571087
t11 = 47.9965544298441
t12 = -89.884456477708
t13 = -57.7703982410123
t14 = -41.7133691226645
t15 = 81.5068760681352
t16 = -96.1676417848876
t17 = 88.1391272257137
t18 = -47.9965544298441
t19 = -37.873644768277
t20 = 96.1676417848876
t21 = -26.0054058547155
t22 = -43.8077642250577
t23 = 83.9503370209273
t24 = -94.0732466824944
t25 = 90.2335223281068
t26 = 68.2423737529783
t27 = -31.2413936106985
t28 = -81.8559419185341
t29 = -99.6583002888762
t30 = -59.8647933434055
t31 = 52.1853446346305
t32 = 42.0624349730633
t33 = 4.01425727958696
t34 = -110.82840750164
t35 = -50.0909495322373
t36 = -45.9021593274509
t37 = -17.9768912955416
t38 = 44.1568300754565
t39 = -6.10865238198015
t40 = 59.8647933434055
t41 = 10.2974425867665
t42 = -4.01425727958696
t43 = -13.7881010907552
t44 = -30.1941960595019
t45 = -33.6848545634906
t46 = -72.0820981073658
t47 = 22.165681500328
t48 = -79.7615468161409
t49 = 8.20304748437335
t50 = 37.873644768277
t51 = 50.0909495322373
t52 = -35.7792496658838
t53 = 94.0732466824944
t54 = 12.7409035395586
t55 = -39.9680398706701
t56 = 15.8824961931484
t57 = -61.9591884457987
t58 = -16.5806278939461
t59 = 34.3829862642883
t60 = -15.8824961931484
t61 = -9.25024503556995
t62 = 98.2620368872808
t63 = 69.9877030049726
t64 = 0.174532925199433
t65 = 561.472420366576
t66 = 32.2885911618951
t67 = -69.9877030049726
t68 = 91.9788515801012
t69 = -1.91986217719376
t70 = 86.0447321233204
t71 = -83.9503370209273
t72 = 63.704517697793
t73 = 2.26892802759263
t74 = 56.3741348394168
t75 = -65.7989128001862
t76 = -55.6760031386191
t77 = 723.43897495165
t78 = 66.1479786505851
t79 = -87.7900613753148
t80 = 100.356431989674
t81 = 64.0535835481919
t82 = 26.0054058547155
t83 = 17.9768912955416
t84 = 30.1941960595019
t85 = -77.6671517137477
t86 = -23.9110107523223
t87 = 20.0712863979348
t88 = 1114.39272739838
t89 = 74.176493209759
t90 = -11.693705988362
t91 = -67.8933079025794
t92 = 72.0820981073658
t93 = 39.9680398706701
t94 = -91.9788515801012
t95 = 61.9591884457987
t96 = 46.2512251778497
t97 = -28.0998009571087
t97 = -28.0998009571087
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