2ctg3x=0 (уравнение)

Найду корень уравнения: 2ctg3x=0

Вы ввели

2*cot(3*x) = 0

$$2 \cot{\left(3 x \right)} = 0$$

Подробное решение

Дано уравнение
$$2 \cot{\left(3 x \right)} = 0$$
преобразуем
$$2 \cot{\left(3 x \right)} - 1 = 0$$
$$2 \cot{\left(3 x \right)} - 1 = 0$$
Сделаем замену
$$w = \cot{\left(3 x \right)}$$
Переносим свободные слагаемые (без w)
из левой части в правую, получим:
$$2 w = 1$$
Разделим обе части ур-ния на 2

w = 1 / (2)

Получим ответ: w = 1/2
делаем обратную замену
$$\cot{\left(3 x \right)} = w$$
подставляем w:

Сумма и произведение корней

сумма

    pi
0 + --
    6 

$$0 + \frac{\pi}{6}$$

=

pi
--
6 

$$\frac{\pi}{6}$$

произведение

  pi
1*--
  6 

$$1 \frac{\pi}{6}$$

=

pi
--
6 

$$\frac{\pi}{6}$$

Быстрый ответ

     pi
x1 = --
     6 

$$x_{1} = \frac{\pi}{6}$$

Численный ответ

x1 = 36.1283155162826

x2 = -71.733032256967

x3 = -16.2315620435473

x4 = 71.733032256967

x5 = -38.2227106186758

x6 = -31.9395253114962

x7 = -14.1371669411541

x8 = 27.7507351067098

x9 = -18.3259571459405

x10 = 90.5825881785057

x11 = 84.2994028713261

x12 = 92.6769832808989

x13 = -91.6297857297023

x14 = -25.6563400043166

x15 = 42.4115008234622

x16 = -95.8185759344887

x17 = 68.5914396033772

x18 = -1.5707963267949

x19 = 58.1194640914112

x20 = -49.7418836818384

x21 = -84.2994028713261

x22 = -34.0339204138894

x23 = 14.1371669411541

x24 = -5.75958653158129

x25 = -75.9218224617533

x26 = -47.6474885794452

x27 = -12.0427718387609

x28 = -58.1194640914112

x29 = 34.0339204138894

x30 = 62.3082542961976

x31 = 31.9395253114962

x32 = -3.66519142918809

x33 = -43.4586983746588

x34 = 86.3937979737193

x35 = -87.4409955249159

x36 = 38.2227106186758

x37 = -7.85398163397448

x38 = -63.3554518473942

x39 = 12.0427718387609

x40 = 22.5147473507269

x41 = 16.2315620435473

x42 = 82.2050077689329

x43 = -65.4498469497874

x44 = 69.6386371545737

x45 = 60.2138591938044

x46 = 95.8185759344887

x47 = 93.7241808320955

x48 = -80.1106126665397

x49 = -45.553093477052

x50 = -27.7507351067098

x51 = -97.9129710368819

x52 = 2.61799387799149

x53 = -89.5353906273091

x54 = 53.9306738866248

x55 = 51.8362787842316

x56 = -85.3466004225227

x57 = -40.317105721069

x58 = -60.2138591938044

x59 = 73.8274273593601

x60 = 29.845130209103

x61 = 100.007366139275

x62 = 3.66519142918809

x63 = 66.497044500984

x64 = 24.60914245312

x65 = -62.3082542961976

x66 = -21.4675497995303

x67 = -53.9306738866248

x68 = -29.845130209103

x69 = -78.0162175641465

x70 = -56.025068989018

x71 = -23.5619449019235

x72 = -82.2050077689329

x73 = 56.025068989018

x74 = 5.75958653158129

x75 = 47.6474885794452

x76 = 78.0162175641465

x77 = 75.9218224617533

x78 = -67.5442420521806

x79 = -93.7241808320955

x80 = 46.6002910282486

x81 = -41.3643032722656

x82 = 40.317105721069

x83 = 97.9129710368819

x84 = -69.6386371545737

x85 = 44.5058959258554

x86 = 64.4026493985908

x87 = -100.007366139275

x88 = 18.3259571459405

x89 = -73.8274273593601

x90 = 88.4881930761125

x91 = 49.7418836818384

x92 = -51.8362787842316

x93 = -19.3731546971371

x94 = 80.1106126665397

x95 = -9.94837673636768

x96 = 9.94837673636768

x97 = 7.85398163397448

x98 = 25.6563400043166

x99 = 20.4203522483337

x100 = -36.1283155162826

График