cos(2*x)=0 (уравнение)

Найду корень уравнения: cos(2*x)=0

Вы ввели

cos(2*x) = 0

$$\cos{\left(2 x \right)} = 0$$

Подробное решение

Дано уравнение
$$\cos{\left(2 x \right)} = 0$$
- это простейшее тригонометрическое ур-ние

с изменением знака при 0

Получим:
$$\cos{\left(2 x \right)} = 0$$
Это ур-ние преобразуется в
$$2 x = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$2 x = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
Или
$$2 x = \pi n + \frac{\pi}{2}$$
$$2 x = \pi n - \frac{\pi}{2}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$2$$
получим ответ:
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{4}$$
$$x_{2} = \frac{\pi n}{2} - \frac{\pi}{4}$$

Сумма и произведение корней

сумма

    pi   3*pi
0 + -- + ----
    4     4  

$$\left(0 + \frac{\pi}{4}\right) + \frac{3 \pi}{4}$$

=

pi

$$\pi$$

произведение

  pi 3*pi
1*--*----
  4   4  

$$\frac{3 \pi}{4} \cdot 1 \frac{\pi}{4}$$

=

    2
3*pi 
-----
  16 

$$\frac{3 \pi^{2}}{16}$$

Быстрый ответ

     pi
x1 = --
     4 

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

     3*pi
x2 = ----
      4  

$$x_{2} = \frac{3 \pi}{4}$$

Численный ответ

x1 = 384.059701901352

x2 = 68.329640215578

x3 = -41.6261026600648

x4 = 3.92699081698724

x5 = 16.4933614313464

x6 = 30.6305283725005

x7 = 11.7809724509617

x8 = -40.0553063332699

x9 = 8.63937979737193

x10 = 88.7499924639117

x11 = -35.3429173528852

x12 = 10.2101761241668

x13 = 27.4889357189107

x14 = -5.49778714378214

x15 = 32.2013246992954

x16 = -27.4889357189107

x17 = 24.3473430653209

x18 = 44.7676953136546

x19 = -38.484510006475

x20 = -62.0464549083984

x21 = -68.329640215578

x22 = 1973.70558461779

x23 = 46.3384916404494

x24 = 66.7588438887831

x25 = 19.6349540849362

x26 = -69.9004365423729

x27 = -55.7632696012188

x28 = 84.037603483527

x29 = 54.1924732744239

x30 = 90.3207887907066

x31 = -79.3252145031423

x32 = 22.776546738526

x33 = 60.4756585816035

x34 = -24.3473430653209

x35 = 5.49778714378214

x36 = -63.6172512351933

x37 = 47.9092879672443

x38 = 52.621676947629

x39 = 98.174770424681

x40 = -90.3207887907066

x41 = 87.1791961371168

x42 = -47.9092879672443

x43 = 49.4800842940392

x44 = -91.8915851175014

x45 = -10.2101761241668

x46 = -54.1924732744239

x47 = 2.35619449019234

x48 = -33.7721210260903

x49 = -18.0641577581413

x50 = -60.4756585816035

x51 = 76.1836218495525

x52 = 77.7544181763474

x53 = -99.7455667514759

x54 = -77.7544181763474

x55 = 162.577419823272

x56 = -93.4623814442964

x57 = -57.3340659280137

x58 = -85.6083998103219

x59 = -3.92699081698724

x60 = -19.6349540849362

x61 = -16.4933614313464

x62 = -32.2013246992954

x63 = 91.8915851175014

x64 = 69.9004365423729

x65 = 38.484510006475

x66 = -82.4668071567321

x67 = -98.174770424681

x68 = 41.6261026600648

x69 = 55.7632696012188

x70 = -12461.9126586273

x71 = -11.7809724509617

x72 = 62.0464549083984

x73 = 82.4668071567321

x74 = -25.9181393921158

x75 = -71.4712328691678

x76 = 18.0641577581413

x77 = 99.7455667514759

x78 = -2.35619449019234

x79 = 63.6172512351933

x80 = -76.1836218495525

x81 = -46.3384916404494

x82 = 85.6083998103219

x83 = 25.9181393921158

x84 = -84.037603483527

x85 = 33.7721210260903

x86 = -49.4800842940392

x87 = 40.0553063332699

x88 = 96.6039740978861

x89 = -13.3517687777566

x90 = 74.6128255227576

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