sin(x)=cos(x) (уравнение)

Найду корень уравнения: sin(x)=cos(x)

Вы ввели

sin(x) = cos(x)

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

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = \cos{\left(x \right)}$$
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

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 

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

Быстрый ответ

     pi
x1 = --
     4 

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

Численный ответ

x1 = 69.9004365423729

x2 = -30.6305283725005

x3 = 98.174770424681

x4 = 7.06858347057703

x5 = 3.92699081698724

x6 = -2.35619449019234

x7 = 38.484510006475

x8 = -80.8960108299372

x9 = -93.4623814442964

x10 = -43.1968989868597

x11 = -46.3384916404494

x12 = -11.7809724509617

x13 = 57.3340659280137

x14 = 19.6349540849362

x15 = -68.329640215578

x16 = 101.316363078271

x17 = 22.776546738526

x18 = 66.7588438887831

x19 = 91.8915851175014

x20 = -21.2057504117311

x21 = -65.1880475619882

x22 = -24.3473430653209

x23 = 44.7676953136546

x24 = -84.037603483527

x25 = -96.6039740978861

x26 = -77.7544181763474

x27 = 79.3252145031423

x28 = 1672.11268987317

x29 = 85.6083998103219

x30 = 29.0597320457056

x31 = -18.0641577581413

x32 = 73.0420291959627

x33 = -27.4889357189107

x34 = 82.4668071567321

x35 = 32.2013246992954

x36 = -14.9225651045515

x37 = 10.2101761241668

x38 = 16.4933614313464

x39 = 51.0508806208341

x40 = -74.6128255227576

x41 = -40.0553063332699

x42 = 54.1924732744239

x43 = 25.9181393921158

x44 = 76.1836218495525

x45 = -5.49778714378214

x46 = 13.3517687777566

x47 = 63.6172512351933

x48 = -33.7721210260903

x49 = -71.4712328691678

x50 = -87.1791961371168

x51 = -36.9137136796801

x52 = -90.3207887907066

x53 = 35.3429173528852

x54 = -99.7455667514759

x55 = -55.7632696012188

x56 = -52.621676947629

x57 = -49.4800842940392

x58 = 60.4756585816035

x59 = 41.6261026600648

x60 = 95.0331777710912

x61 = -8.63937979737193

x62 = 0.785398163397448

x63 = -62.0464549083984

x64 = 88.7499924639117

x65 = -228.550865548657

x66 = -58.9048622548086

x67 = 47.9092879672443

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