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tg(17x)=sqrt3/3 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
              ___
            \/ 3 
tan(17*x) = -----
              3  
$$\tan{\left(17 x \right)} = \frac{\sqrt{3}}{3}$$
Solución detallada
Tenemos la ecuación
$$\tan{\left(17 x \right)} = \frac{\sqrt{3}}{3}$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$17 x = \pi n + \operatorname{atan}{\left(\frac{\sqrt{3}}{3} \right)}$$
O
$$17 x = \pi n + \frac{\pi}{6}$$
, donde n es cualquier número entero
Dividamos ambos miembros de la ecuación obtenida en
$$17$$
obtenemos la respuesta:
$$x_{1} = \frac{\pi n}{17} + \frac{\pi}{102}$$
Gráfica
Respuesta rápida [src]
      pi
x1 = ---
     102
$$x_{1} = \frac{\pi}{102}$$
x1 = pi/102
Suma y producto de raíces [src]
suma
 pi
---
102
$$\frac{\pi}{102}$$
=
 pi
---
102
$$\frac{\pi}{102}$$
producto
 pi
---
102
$$\frac{\pi}{102}$$
=
 pi
---
102
$$\frac{\pi}{102}$$
pi/102
Respuesta numérica [src]
x1 = -83.6834043117987
x2 = -19.7427538328535
x3 = -79.9874129546343
x4 = 28.3051338102845
x5 = -3.84999099704632
x6 = 84.2994028713261
x7 = 44.0130970782335
x8 = 34.2187199817476
x9 = 76.1682218855643
x10 = 42.3499009675095
x11 = 14.2603666530596
x12 = -97.7281714690237
x13 = 92.2457842892297
x14 = -11.9811719828081
x15 = -61.6922557366702
x16 = -89.7817900511201
x17 = 87.9953942284906
x18 = 52.1442780639953
x19 = -31.754725743638
x20 = 41.0563039925019
x21 = -55.778669565207
x22 = -73.7042276474547
x23 = -99.7609667154641
x24 = 80.2338123784452
x25 = 16.2931618995
x26 = -81.6506090653583
x27 = 19.9891532566645
x28 = -85.7161995582392
x29 = -95.6953762225832
x30 = -23.9931438935926
x31 = -36.0051158043771
x32 = -13.8291676613904
x33 = -87.7489948046796
x34 = 18.1411575780822
x35 = -63.7250509831106
x36 = 62.3082542961976
x37 = 12.2275714066191
x38 = -15.8619629078308
x39 = 26.2723385638441
x40 = 94.2785795356702
x41 = 89.6585903392146
x42 = 38.2843104746286
x43 = 70.2546357141012
x44 = -7.730781922069
x45 = 63.7866508390633
x46 = 48.2634871389726
x47 = -53.7458743187666
x48 = -28.0587343864735
x49 = -2.00199531846408
x50 = 74.3202262069821
x51 = 82.2666076248857
x52 = -77.7698181403356
x53 = 50.2962823854131
x54 = 103.518557928581
x55 = -43.7666976544225
x56 = 32.001125167449
x57 = 58.2426638033167
x58 = 96.3113747821106
x59 = -70.0082362902902
x60 = -21.775549079294
x61 = 6.31398523515596
x62 = -27.6891352507571
x63 = 66.004245653362
x64 = 0.58519863155104
x65 = 24.2395433174036
x66 = -37.8531114829594
x67 = 46.2306918925322
x68 = -54.6698721580577
x69 = 60.2754590497571
x70 = 8.53158004945463
x71 = -41.7339024079821
x72 = 53.9922737425775
x73 = 72.2874309605416
x74 = 2.24839474227505
x75 = -47.8322881473034
x76 = 78.0162175641465
x77 = -45.9842924687212
x78 = 86.1473985499083
x79 = -17.7099585864131
x80 = -5.69798667562855
x81 = -71.8562319688724
x82 = -49.6802838258857
x83 = 40.317105721069
x84 = -91.9993848654187
x85 = -9.76357716850946
x86 = -75.7370228938951
x87 = 100.007366139275
x88 = -65.7578462295511
x89 = 56.025068989018
x90 = -91.2601865939858
x91 = 22.0219485031049
x92 = -51.7130790723261
x93 = -39.7011071615416
x94 = 10.0099765923204
x95 = 68.2218404676607
x96 = -57.9962643795057
x97 = -67.9754410438497
x98 = 4.2811899887155
x99 = -29.7219304971976
x100 = 36.2515152281881
x100 = 36.2515152281881