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2sin(3x-3)+1=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
2*sin(3*x - 3) + 1 = 0
2sin⁡(3x−3)+1=02 \sin{\left(3 x - 3 \right)} + 1 = 0
Simplificar
Solución detallada
Tenemos la ecuación
2sin⁡(3x−3)+1=02 \sin{\left(3 x - 3 \right)} + 1 = 0
es la ecuación trigonométrica más simple
Transportemos 1 al miembro derecho de la ecuación

cambiando el signo de 1

Obtenemos:
2sin⁡(3x−3)=−12 \sin{\left(3 x - 3 \right)} = -1
Dividamos ambos miembros de la ecuación en 2

La ecuación se convierte en
sin⁡(3x−3)=−12\sin{\left(3 x - 3 \right)} = - \frac{1}{2}
Esta ecuación se reorganiza en
3x−3=2πn+asin⁡(−12)3 x - 3 = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{2} \right)}
3x−3=2πn−asin⁡(−12)+π3 x - 3 = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{2} \right)} + \pi
O
3x−3=2πn−π63 x - 3 = 2 \pi n - \frac{\pi}{6}
3x−3=2πn+7π63 x - 3 = 2 \pi n + \frac{7 \pi}{6}
, donde n es cualquier número entero
Transportemos
−3-3
al miembro derecho de la ecuación
con el signo opuesto, en total:
3x=2πn−π6+33 x = 2 \pi n - \frac{\pi}{6} + 3
3x=2πn+3+7π63 x = 2 \pi n + 3 + \frac{7 \pi}{6}
Dividamos ambos miembros de la ecuación obtenida en
33
obtenemos la respuesta:
x1=2πn3−π18+1x_{1} = \frac{2 \pi n}{3} - \frac{\pi}{18} + 1
x2=2πn3+1+7π18x_{2} = \frac{2 \pi n}{3} + 1 + \frac{7 \pi}{18}
Gráfica
0-80-60-40-2020406080-1001005-5
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
         pi
x1 = 1 - --
         18
x1=1−π18x_{1} = 1 - \frac{\pi}{18} 
         7*pi
x2 = 1 + ----
          18
x2=1+7π18x_{2} = 1 + \frac{7 \pi}{18} 
x2 = 1 + 7*pi/18
Suma y producto de raíces [src] 
suma
    pi       7*pi
1 - -- + 1 + ----
    18        18
(1−π18)+(1+7π18)\left(1 - \frac{\pi}{18}\right) + \left(1 + \frac{7 \pi}{18}\right) 
=
    pi
2 + --
    3
π3+2\frac{\pi}{3} + 2 
producto
/    pi\ /    7*pi\
|1 - --|*|1 + ----|
\    18/ \     18 /
(1−π18)(1+7π18)\left(1 - \frac{\pi}{18}\right) \left(1 + \frac{7 \pi}{18}\right) 
=
(18 - pi)*(18 + 7*pi)
---------------------
         324
(18−π)(18+7π)324\frac{\left(18 - \pi\right) \left(18 + 7 \pi\right)}{324} 
(18 - pi)*(18 + 7*pi)/324
Respuesta numérica [src] 
x1 = -57.8175957922089
x2 = -87.8372589265114
x3 = 28.0526034059121
x4 = 83.9031394697307
x5 = -97.6111027376796
x6 = 19.6750229963393
x7 = -11.7409035395586
x8 = -68.2895713041749
x9 = -79.4596785169386
x10 = -94.120444233691
x11 = -92.0260491312978
x12 = 57.3741348394168
x13 = -18.0240888467382
x14 = 88.091929674517
x15 = 17593.0461954768
x16 = -30.5904594610974
x17 = 74.1292956585624
x18 = -43.8549617762543
x19 = -53.6288055874225
x20 = -48.0437519810407
x21 = 72.0349005561692
x22 = 94.3751149816966
x23 = 32.2413936106985
x24 = -64.1007810993885
x25 = -81.5540736193318
x26 = 98.563905186483
x27 = -62.0063859969953
x28 = 65.7517152489896
x29 = -6.15584993317675
x30 = -24.3072741539178
x31 = 90.1863247769102
x32 = -83.648468721725
x33 = 37.8264472170804
x34 = 122.300383013606
x35 = 67.8461103513828
x36 = 46.2040276266531
x37 = -78.7615468161409
x38 = 76.2236907609556
x39 = 21.7694180987325
x40 = -70.3839664065681
x41 = 25.9582083035189
x42 = 30.1469985083053
x43 = 2.22173047639603
x44 = 60.8647933434055
x45 = -77.3652834145454
x46 = 39.9208423194736
x47 = -22.9110107523223
x48 = -1.96705972839036
x49 = -45.9493568786475
x50 = 44.1096325242599
x51 = 23.8638132011257
x52 = 593.539281052075
x53 = -50.1381470834339
x54 = -59.9119908946021
x55 = -89.9316540289046
x56 = 92.2807198793034
x57 = 10.5993108859688
x58 = -26.401669256311
x59 = 36.4301838154849
x60 = -20.1184839491314
x61 = 52.4872129338327
x62 = 63.6573201465964
x63 = -99.7054978400728
x64 = 6.41052068118242
x65 = 48.2984227290463
x66 = -13.8352986419518
x67 = -15.929693744345
x68 = 80.412480965742
x69 = 50.3928178314395
x70 = -33.3829862642883
x71 = 96.4695100840898
x72 = -41.7605666738611
x73 = -9.64650843716541
x74 = 8.50491578357562
x75 = -37.5717764690747
x76 = 85.9975345721239
x77 = 78.3180858633488
x78 = 100.658300288876
x79 = 17.5806278939461
x80 = -22.2128790515246
x81 = 4.31612557878923
x82 = 34.3357887130917
x83 = -55.7232006898157
x84 = -56.4213323906134
x85 = -66.1951762017817
x86 = 69.940505453776
x87 = 54.5816080362259
x88 = 42.0152374218667
x89 = -39.6661715714679
x90 = 0.127335374002835
x91 = 13.3918376891597
x92 = -85.7428638241182
x93 = -35.4773813666815
x94 = -4.06145483078356
x94 = -4.06145483078356
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