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sin(x)=-1/3

sin(x)=-1/3 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
sin(x) = -1/3
$$\sin{\left(x \right)} = - \frac{1}{3}$$
Solución detallada
Tenemos la ecuación
$$\sin{\left(x \right)} = - \frac{1}{3}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{3} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{3} \right)} + \pi$$
O
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{3} \right)}$$
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{3} \right)} + \pi$$
, donde n es cualquier número entero
Gráfica
Suma y producto de raíces [src]
suma
pi + asin(1/3) - asin(1/3)
$$- \operatorname{asin}{\left(\frac{1}{3} \right)} + \left(\operatorname{asin}{\left(\frac{1}{3} \right)} + \pi\right)$$
=
pi
$$\pi$$
producto
(pi + asin(1/3))*(-asin(1/3))
$$\left(\operatorname{asin}{\left(\frac{1}{3} \right)} + \pi\right) \left(- \operatorname{asin}{\left(\frac{1}{3} \right)}\right)$$
=
-(pi + asin(1/3))*asin(1/3)
$$- \left(\operatorname{asin}{\left(\frac{1}{3} \right)} + \pi\right) \operatorname{asin}{\left(\frac{1}{3} \right)}$$
-(pi + asin(1/3))*asin(1/3)
Respuesta rápida [src]
x1 = pi + asin(1/3)
$$x_{1} = \operatorname{asin}{\left(\frac{1}{3} \right)} + \pi$$
x2 = -asin(1/3)
$$x_{2} = - \operatorname{asin}{\left(\frac{1}{3} \right)}$$
x2 = -asin(1/3)
Respuesta numérica [src]
x1 = 9.7646148702235
x2 = -69.4548752884296
x3 = 34.8973560989418
x4 = 16.0478001774031
x5 = -358.481399418691
x6 = -27.934496972854
x7 = 68.7752014695213
x8 = 31.0760896264438
x9 = -56.8885046740704
x10 = 301.253057835166
x11 = 28.6141707917623
x12 = -44.3221340597112
x13 = -90.7663500446499
x14 = -9.08494105131526
x15 = -21.6513116656744
x16 = -31.7557634453521
x17 = -46.7840528943928
x18 = 56.2088308551622
x19 = 81.3415720838805
x20 = 53.7469120204806
x21 = 345.235354985423
x22 = -40.5008675872132
x23 = -38.0389487525316
x24 = -25.4725781381725
x25 = 41.1805414061214
x26 = -34.2176822800336
x27 = -15.3681263584948
x28 = -12.9062075238133
x29 = 144.173425155676
x30 = 78.879653249199
x31 = 85.1628385563785
x32 = -84.4831647374703
x33 = -65.6336088159315
x34 = 47.463726713301
x35 = -63.17168998125
x36 = 3.48142956304392
x37 = 87.6247573910601
x38 = 43.642460240803
x39 = 93.9079426982397
x40 = -94.5876165171479
x41 = 5.94334839772546
x42 = -59.350423508752
x43 = -88.3044312099683
x44 = 18.5097190120846
x45 = 24.7929043192642
x46 = -100.870801824328
x47 = 100.191128005419
x48 = -53.0672382015724
x49 = 62.4920161623417
x50 = -0.339836909454122
x51 = -97.0495353518295
x52 = -19.1893928309929
x53 = 75.0583867767009
x54 = -71.9167941231111
x55 = -2.80175574413567
x56 = 37.3592749336234
x57 = 60.0300973276602
x58 = 49.9256455479826
x59 = 72.5964679420194
x60 = -6.62302221663371
x61 = 66.3132826348398
x62 = -75.7380605956092
x63 = 22.3309854845827
x64 = -78.1999794302907
x65 = 91.4460238635581
x66 = 97.7292091707377
x67 = -50.6053193668908
x68 = 3047.00503707265
x69 = -82.0212459027887
x70 = 12.2265337049051
x70 = 12.2265337049051
Gráfico
sin(x)=-1/3 la ecuación