Ctgx=1 (уравнение)

Найду корень уравнения: Ctgx=1

Вы ввели

cot(x) = 1

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

Подробное решение

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

Быстрый ответ

     pi
x1 = --
     4 

$$x_{1} = \frac{\pi}{4}$$

Сумма и произведение корней

сумма

    pi
0 + --
    4 

$$0 + \frac{\pi}{4}$$

=

pi
--
4 

$$\frac{\pi}{4}$$

произведение

  pi
1*--
  4 

$$1 \frac{\pi}{4}$$

=

pi
--
4 

$$\frac{\pi}{4}$$

Численный ответ

x1 = -11.7809724509617

x2 = 69.9004365423729

x3 = -30.6305283725005

x4 = 95.0331777710912

x5 = -71.4712328691678

x6 = -90.3207887907066

x7 = 51.0508806208341

x8 = 25.9181393921158

x9 = 0.785398163397448

x10 = 35.3429173528852

x11 = -33.7721210260903

x12 = -93.4623814442964

x13 = -18.0641577581413

x14 = 19.6349540849362

x15 = -55.7632696012188

x16 = 7.06858347057703

x17 = 73.0420291959627

x18 = -43.1968989868597

x19 = -14.9225651045515

x20 = 57.3340659280137

x21 = -8.63937979737193

x22 = 98.174770424681

x23 = 47.9092879672443

x24 = -46.3384916404494

x25 = -74.6128255227576

x26 = 29.0597320457056

x27 = -21.2057504117311

x28 = -68.329640215578

x29 = -99.7455667514759

x30 = 79.3252145031423

x31 = -77.7544181763474

x32 = -84.037603483527

x33 = -27.4889357189107

x34 = 85.6083998103219

x35 = -96.6039740978861

x36 = 10.2101761241668

x37 = 13.3517687777566

x38 = 60.4756585816035

x39 = 3.92699081698724

x40 = -36.9137136796801

x41 = -52.621676947629

x42 = 32.2013246992954

x43 = -62.0464549083984

x44 = -58.9048622548086

x45 = 22.776546738526

x46 = 16.4933614313464

x47 = 41.6261026600648

x48 = -80.8960108299372

x49 = 54.1924732744239

x50 = -5.49778714378214

x51 = -49.4800842940392

x52 = 82.4668071567321

x53 = -65.1880475619882

x54 = 91.8915851175014

x55 = 66.7588438887831

x56 = 76.1836218495525

x57 = -87.1791961371168

x58 = -24.3473430653209

x59 = 63.6172512351933

x60 = -2.35619449019234

x61 = 38.484510006475

x62 = 44.7676953136546

x63 = 88.7499924639117

x64 = -40.0553063332699

График