sin(x)-cos(x)=0 (уравнение)

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

Вы ввели

sin(x) - cos(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 

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

=

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 = -228.550865548657

x14 = -18.0641577581413

x15 = 19.6349540849362

x16 = -55.7632696012188

x17 = 7.06858347057703

x18 = 73.0420291959627

x19 = -43.1968989868597

x20 = -14.9225651045515

x21 = 57.3340659280137

x22 = -8.63937979737193

x23 = 98.174770424681

x24 = 47.9092879672443

x25 = -46.3384916404494

x26 = -74.6128255227576

x27 = 1672.11268987317

x28 = 29.0597320457056

x29 = -21.2057504117311

x30 = -68.329640215578

x31 = -99.7455667514759

x32 = 79.3252145031423

x33 = -77.7544181763474

x34 = -84.037603483527

x35 = -27.4889357189107

x36 = 85.6083998103219

x37 = -96.6039740978861

x38 = 10.2101761241668

x39 = 13.3517687777566

x40 = 60.4756585816035

x41 = 3.92699081698724

x42 = -36.9137136796801

x43 = -52.621676947629

x44 = 32.2013246992954

x45 = -62.0464549083984

x46 = -58.9048622548086

x47 = 22.776546738526

x48 = 16.4933614313464

x49 = 41.6261026600648

x50 = -80.8960108299372

x51 = 54.1924732744239

x52 = -5.49778714378214

x53 = 101.316363078271

x54 = -49.4800842940392

x55 = 82.4668071567321

x56 = -65.1880475619882

x57 = 66.7588438887831

x58 = 76.1836218495525

x59 = 91.8915851175014

x60 = -87.1791961371168

x61 = -24.3473430653209

x62 = 63.6172512351933

x63 = -2.35619449019234

x64 = 38.484510006475

x65 = 44.7676953136546

x66 = 88.7499924639117

x67 = -40.0553063332699

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