Sr Examen

Otras calculadoras

sin(3*x)*sin(x)=1/2 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

v

Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src] 
sin(3*x)*sin(x) = 1/2
$$\sin{\left(x \right)} \sin{\left(3 x \right)} = \frac{1}{2}$$
Simplificar
Gráfica
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
  5*pi   3*pi   pi   pi   pi   pi   3*pi   5*pi
- ---- - ---- - -- - -- + -- + -- + ---- + ----
   6      4     4    6    6    4     4      6
$$\left(\left(\left(\left(\left(\left(- \frac{5 \pi}{6} - \frac{3 \pi}{4}\right) - \frac{\pi}{4}\right) - \frac{\pi}{6}\right) + \frac{\pi}{6}\right) + \frac{\pi}{4}\right) + \frac{3 \pi}{4}\right) + \frac{5 \pi}{6}$$ 
=
0
$$0$$ 
producto
-5*pi -3*pi -pi  -pi  pi pi 3*pi 5*pi
-----*-----*----*----*--*--*----*----
  6     4    4    6   6  4   4    6
$$\frac{5 \pi}{6} \frac{3 \pi}{4} \frac{\pi}{4} \frac{\pi}{6} \cdot - \frac{\pi}{6} \cdot - \frac{\pi}{4} \cdot - \frac{5 \pi}{6} \left(- \frac{3 \pi}{4}\right)$$ 
=
     8
25*pi 
------
36864
$$\frac{25 \pi^{8}}{36864}$$ 
25*pi^8/36864
Respuesta rápida [src] 
     -5*pi
x1 = -----
       6
$$x_{1} = - \frac{5 \pi}{6}$$ 
     -3*pi
x2 = -----
       4
$$x_{2} = - \frac{3 \pi}{4}$$ 
     -pi 
x3 = ----
      4
$$x_{3} = - \frac{\pi}{4}$$ 
     -pi 
x4 = ----
      6
$$x_{4} = - \frac{\pi}{6}$$ 
     pi
x5 = --
     6
$$x_{5} = \frac{\pi}{6}$$ 
     pi
x6 = --
     4
$$x_{6} = \frac{\pi}{4}$$ 
     3*pi
x7 = ----
      4
$$x_{7} = \frac{3 \pi}{4}$$ 
     5*pi
x8 = ----
      6
$$x_{8} = \frac{5 \pi}{6}$$ 
x8 = 5*pi/6
Respuesta numérica [src] 
x1 = 10.2101761241668
x2 = -38.2227106186758
x3 = 96.6039740978861
x4 = 68.329640215578
x5 = -53.9306738866248
x6 = -91.8915851175014
x7 = 3.92699081698724
x8 = -36.9137136796801
x9 = -11.7809724509617
x10 = -24.3473430653209
x11 = 66.497044500984
x12 = 63.6172512351933
x13 = 69.9004365423729
x14 = 98.174770424681
x15 = 41.6261026600648
x16 = 84.2994028713261
x17 = -16.2315620435473
x18 = 38.2227106186758
x19 = 242.688032489812
x20 = -33.7721210260903
x21 = 40.317105721069
x22 = -57.3340659280137
x23 = -46.3384916404494
x24 = -107.337748997651
x25 = 49.7418836818384
x26 = 27.7507351067098
x27 = -18.0641577581413
x28 = 71.4712328691678
x29 = 93.4623814442964
x30 = -69.9004365423729
x31 = 2.35619449019234
x32 = -19.6349540849362
x33 = 24.3473430653209
x34 = -68.329640215578
x35 = -71.733032256967
x36 = 44.5058959258554
x37 = 88.4881930761125
x38 = -85.6083998103219
x39 = -77.7544181763474
x40 = 78.0162175641465
x41 = -90.3207887907066
x42 = 90.3207887907066
x43 = 60.2138591938044
x44 = 74.6128255227576
x45 = -5.75958653158129
x46 = 30.6305283725005
x47 = -43.1968989868597
x48 = 8.63937979737193
x49 = -82.2050077689329
x50 = 5.75958653158129
x51 = -31.9395253114962
x52 = -62.0464549083984
x53 = 19.6349540849362
x54 = 12.0427718387609
x55 = -14.9225651045515
x56 = 82.2050077689329
x57 = -63.6172512351933
x58 = 54.1924732744239
x59 = -99.7455667514759
x60 = -35.3429173528852
x61 = -21.2057504117311
x62 = -60.2138591938044
x63 = 46.3384916404494
x64 = -93.7241808320955
x65 = -32.2013246992954
x66 = -75.9218224617533
x67 = 0.785398163397448
x68 = -41.6261026600648
x69 = 85.6083998103219
x70 = -49.7418836818384
x71 = 47.9092879672443
x72 = 34.0339204138894
x73 = -55.7632696012188
x74 = -47.9092879672443
x75 = 52.621676947629
x76 = -97.9129710368819
x77 = -56.025068989018
x78 = -65.1880475619882
x79 = 32.2013246992954
x80 = 56.025068989018
x81 = 22.776546738526
x82 = 100.007366139275
x83 = -0.785398163397448
x84 = -84.037603483527
x85 = -79.3252145031423
x86 = -13.3517687777566
x87 = -27.7507351067098
x88 = 62.3082542961976
x89 = 76.1836218495525
x90 = -2.35619449019234
x91 = 25.9181393921158
x92 = 16.2315620435473
x93 = -40.0553063332699
x94 = -9.94837673636768
x95 = 18.3259571459405
x96 = 91.8915851175014
x96 = 91.8915851175014
    © Sr Examen – Калькулятор