cos(x)+sin(x)=0 (уравнение)

Найду корень уравнения: cos(x)+sin(x)=0

Вы ввели

cos(x) + sin(x) = 0

$$\sin{\left(x \right)} + \cos{\left(x \right)} = 0$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} + \cos{\left(x \right)} = 0$$
преобразуем:
$$\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} = -1$$
или
$$\tan{\left(x \right)} = -1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{atan}{\left(1 \right)}$$
Или
$$x = \pi n + \frac{\pi}{4}$$
, где n - любое целое число

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 = 93.4623814442964

x2 = -57.3340659280137

x3 = -41.6261026600648

x4 = -51.0508806208341

x5 = -69.9004365423729

x6 = 68.329640215578

x7 = -44.7676953136546

x8 = -29.0597320457056

x9 = 84.037603483527

x10 = 65.1880475619882

x11 = -85.6083998103219

x12 = -3.92699081698724

x13 = -19.6349540849362

x14 = 30.6305283725005

x15 = -16.4933614313464

x16 = 90.3207887907066

x17 = -79.3252145031423

x18 = -32.2013246992954

x19 = 11.7809724509617

x20 = 99.7455667514759

x21 = 5.49778714378214

x22 = -7.06858347057703

x23 = -22.776546738526

x24 = -63.6172512351933

x25 = -88.7499924639117

x26 = 58.9048622548086

x27 = 351.072979038659

x28 = 8.63937979737193

x29 = 52.621676947629

x30 = -76.1836218495525

x31 = -107.59954838545

x32 = 87.1791961371168

x33 = -82.4668071567321

x34 = 36.9137136796801

x35 = -98.174770424681

x36 = -47.9092879672443

x37 = -95.0331777710912

x38 = 49.4800842940392

x39 = -91.8915851175014

x40 = -35.3429173528852

x41 = -54.1924732744239

x42 = 2.35619449019234

x43 = -10.2101761241668

x44 = 27.4889357189107

x45 = 80.8960108299372

x46 = -0.785398163397448

x47 = 24.3473430653209

x48 = -66.7588438887831

x49 = -73.0420291959627

x50 = 55.7632696012188

x51 = -60.4756585816035

x52 = -25.9181393921158

x53 = -38.484510006475

x54 = 33.7721210260903

x55 = 77.7544181763474

x56 = 43.1968989868597

x57 = 62.0464549083984

x58 = 40.0553063332699

x59 = 96.6039740978861

x60 = -13.3517687777566

x61 = 74.6128255227576

x62 = 21.2057504117311

x63 = 71.4712328691678

x64 = 46.3384916404494

x65 = 14.9225651045515

x66 = 18.0641577581413

График