tg3x-1=0 (уравнение)

Найду корень уравнения: tg3x-1=0

Вы ввели

tan(3*x) - 1 = 0

$$\tan{\left(3 x \right)} - 1 = 0$$

Подробное решение

Дано уравнение
$$\tan{\left(3 x \right)} - 1 = 0$$
- это простейшее тригонометрическое ур-ние

Перенесём -1 в правую часть ур-ния

с изменением знака при -1

Получим:
$$\tan{\left(3 x \right)} - 1 + 1 = 1$$
Это ур-ние преобразуется в
$$3 x = \pi n + \operatorname{atan}{\left(1 \right)}$$
Или
$$3 x = \pi n + \frac{\pi}{4}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$3$$
получим ответ:
$$x_{1} = \frac{\pi n}{3} + \frac{\pi}{12}$$

Быстрый ответ

     pi
x1 = --
     12

$$x_{1} = \frac{\pi}{12}$$

Сумма и произведение корней

сумма

    pi
0 + --
    12

$$0 + \frac{\pi}{12}$$

=

pi
--
12

$$\frac{\pi}{12}$$

произведение

  pi
1*--
  12

$$1 \frac{\pi}{12}$$

=

pi
--
12

$$\frac{\pi}{12}$$

Численный ответ

x1 = 56.8104671524154

x2 = 24.3473430653209

x3 = -39.5317075576716

x4 = -23.8237442897226

x5 = 68.329640215578

x6 = 26.4417381677141

x7 = -79.3252145031423

x8 = -3.92699081698724

x9 = -63.6172512351933

x10 = 52.621676947629

x11 = -59.4284610304069

x12 = -43.720497762458

x13 = -21.7293491873294

x14 = 50.5272818452358

x15 = -28.012534494509

x16 = -69.9004365423729

x17 = 48.4328867428426

x18 = 54.7160720500222

x19 = -35.3429173528852

x20 = -47.9092879672443

x21 = 92.4151838930998

x22 = 10.7337748997651

x23 = 4.45058959258554

x24 = -50.0036830696375

x25 = 0.261799387799149

x26 = 22.2529479629277

x27 = -52.0980781720307

x28 = -53.1452757232273

x29 = -33.248522250492

x30 = -75.1364242983559

x31 = 86.1319985859202

x32 = -15.4461638801498

x33 = 18.0641577581413

x34 = 42.1497014356631

x35 = 58.9048622548086

x36 = -11.2573736753634

x37 = -83.5140047079287

x38 = 30.6305283725005

x39 = -31.1541271480988

x40 = -65.7116463375865

x41 = 13.8753675533549

x42 = -96.0803753222878

x43 = 40.0553063332699

x44 = -17.540558982543

x45 = -25.9181393921158

x46 = 59.9520598060052

x47 = -74.0892267471593

x48 = 34.8193185772869

x49 = 88.2263936883134

x50 = -91.8915851175014

x51 = -1.83259571459405

x52 = 100.792764302673

x53 = -37.4373124552784

x54 = -41.6261026600648

x55 = 80.8960108299372

x56 = 32.7249234748937

x57 = 44.2440965380563

x58 = 28.5361332701073

x59 = -71.9948316447661

x60 = -30.1069295969022

x61 = -6.02138591938044

x62 = 2.35619449019234

x63 = -85.6083998103219

x64 = 76.7072206251508

x65 = -81.4196096055355

x66 = 64.1408500107916

x67 = 72.5184304203644

x68 = 90.3207887907066

x69 = 66.2352451131848

x70 = 94.5095789954929

x71 = 46.3384916404494

x72 = 15.9697626557481

x73 = 74.6128255227576

x74 = 8.63937979737193

x75 = 70.4240353179712

x76 = 96.6039740978861

x77 = 36.9137136796801

x78 = 12.8281700021583

x79 = -55.2396708256205

x80 = 84.037603483527

x81 = 98.6983692002793

x82 = -77.2308194007491

x83 = 62.0464549083984

x84 = -93.9859802198946

x85 = 20.1585528605345

x86 = -89.7971900151083

x87 = -99.2219679758776

x88 = -8.11578102177363

x89 = -45.8148928648512

x90 = 81.9432083811338

x91 = -13.3517687777566

x92 = -9.16297857297023

x93 = -61.5228561328001

x94 = 37.9609112308767

x95 = -67.8060414399797

x96 = 78.801615727544

x97 = -97.1275728734844

x98 = 6.54498469497874

x99 = -57.3340659280137

x100 = -87.7027949127151

x101 = -19.6349540849362

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