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 

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

=

-pi 
----
 4  

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

произведение

  -pi 
1*----
   4  

$$1 \left(- \frac{\pi}{4}\right)$$

=

-pi 
----
 4  

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

Численный ответ

x1 = -47.9092879672443

x2 = -35.3429173528852

x3 = -0.785398163397448

x4 = 11.7809724509617

x5 = 84.037603483527

x6 = 18.0641577581413

x7 = -95.0331777710912

x8 = -54.1924732744239

x9 = -63.6172512351933

x10 = 5.49778714378214

x11 = 49.4800842940392

x12 = -29.0597320457056

x13 = 93.4623814442964

x14 = 80.8960108299372

x15 = -44.7676953136546

x16 = 68.329640215578

x17 = -19.6349540849362

x18 = 43.1968989868597

x19 = 24.3473430653209

x20 = 14.9225651045515

x21 = 8.63937979737193

x22 = 21.2057504117311

x23 = -98.174770424681

x24 = -10.2101761241668

x25 = -85.6083998103219

x26 = -82.4668071567321

x27 = -76.1836218495525

x28 = 27.4889357189107

x29 = 62.0464549083984

x30 = -32.2013246992954

x31 = 2.35619449019234

x32 = 40.0553063332699

x33 = -41.6261026600648

x34 = 46.3384916404494

x35 = -25.9181393921158

x36 = 71.4712328691678

x37 = 55.7632696012188

x38 = -79.3252145031423

x39 = 77.7544181763474

x40 = -38.484510006475

x41 = 52.621676947629

x42 = -57.3340659280137

x43 = 74.6128255227576

x44 = -60.4756585816035

x45 = -16.4933614313464

x46 = 99.7455667514759

x47 = -69.9004365423729

x48 = -13.3517687777566

x49 = 65.1880475619882

x50 = -73.0420291959627

x51 = -3.92699081698724

x52 = -7.06858347057703

x53 = -88.7499924639117

x54 = 87.1791961371168

x55 = -22.776546738526

x56 = -51.0508806208341

x57 = 33.7721210260903

x58 = 36.9137136796801

x59 = 58.9048622548086

x60 = -66.7588438887831

x61 = -91.8915851175014

x62 = 30.6305283725005

x63 = 96.6039740978861

x64 = 90.3207887907066

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