ctg(x)=1/3 (уравнение)

Найду корень уравнения: ctg(x)=1/3

Вы ввели

cot(x) = 1/3

$$\cot{\left(x \right)} = \frac{1}{3}$$

Подробное решение

Дано уравнение
$$\cot{\left(x \right)} = \frac{1}{3}$$
преобразуем
$$\cot{\left(x \right)} - \frac{1}{3} = 0$$
$$\cot{\left(x \right)} - \frac{1}{3} = 0$$
Сделаем замену
$$w = \cot{\left(x \right)}$$
Переносим свободные слагаемые (без w)
из левой части в правую, получим:
$$w = \frac{1}{3}$$
Получим ответ: w = 1/3
делаем обратную замену
$$\cot{\left(x \right)} = w$$
подставляем w:

Быстрый ответ

x1 = acot(1/3)

$$x_{1} = \operatorname{acot}{\left(\frac{1}{3} \right)}$$

Сумма и произведение корней

сумма

0 + acot(1/3)

$$0 + \operatorname{acot}{\left(\frac{1}{3} \right)}$$

=

acot(1/3)

$$\operatorname{acot}{\left(\frac{1}{3} \right)}$$

произведение

1*acot(1/3)

$$1 \operatorname{acot}{\left(\frac{1}{3} \right)}$$

=

acot(1/3)

$$\operatorname{acot}{\left(\frac{1}{3} \right)}$$

Численный ответ

x1 = 32.6649723082962

x2 = 35.806564961886

x3 = -55.299621992218

x4 = -89.8571411817058

x5 = -23.8836954563201

x6 = -1.89254688119154

x7 = 1.24904577239825

x8 = -64.7243999529874

x9 = 67.2224914977839

x10 = 95.496825380092

x11 = 92.3552327265023

x12 = -5.03413953478133

x13 = 60.9393061906043

x14 = -8.17573218837112

x15 = 79.7888621121431

x16 = 64.0808988441941

x17 = -77.2907705673466

x18 = 73.5056768049635

x19 = -42.7332513778588

x20 = -33.3084734170895

x21 = -96.1403264888853

x22 = 98.6384180336818

x23 = 51.5145282298349

x24 = -83.5739558745262

x25 = 86.0720474193227

x26 = 20.098601693937

x27 = 10.6738237331676

x28 = 16.9570090403472

x29 = -36.4500660706793

x30 = 13.8154163867574

x31 = -99.2819191424751

x32 = 82.9304547657329

x33 = -17.6005101491405

x34 = 57.7977135370145

x35 = -39.5916587242691

x36 = 70.3640841513737

x37 = -52.1580293386282

x38 = -58.4412146458078

x39 = 7.53223107957784

x40 = 23.2401943475268

x41 = -30.1668807634997

x42 = -71.007585260167

x43 = -80.4323632209364

x44 = 38.9481576154758

x45 = -20.7421028027303

x46 = -27.0252881099099

x47 = 45.2313429226554

x48 = 42.0897502690656

x49 = -86.715548528116

x50 = 48.3729355762452

x51 = -74.1491779137568

x52 = 54.6561208834247

x53 = 89.2136400729125

x54 = 4.39063842598805

x55 = -49.0164366850384

x56 = -45.8748440314486

x57 = -14.4589174955507

x58 = 26.3817870011166

x59 = -61.5828072993976

x60 = -92.9987338352955

x61 = 29.5233796547064

x62 = 76.6472694585533

x63 = -11.3173248419609

x64 = -67.8659926065772

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