cos6x=0 (уравнение)

Найду корень уравнения: cos6x=0

Вы ввели

cos(6*x) = 0

$$\cos{\left(6 x \right)} = 0$$

Подробное решение

Дано уравнение
$$\cos{\left(6 x \right)} = 0$$
- это простейшее тригонометрическое ур-ние

с изменением знака при 0

Получим:
$$\cos{\left(6 x \right)} = 0$$
Это ур-ние преобразуется в
$$6 x = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$6 x = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
Или
$$6 x = \pi n + \frac{\pi}{2}$$
$$6 x = \pi n - \frac{\pi}{2}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$6$$
получим ответ:
$$x_{1} = \frac{\pi n}{6} + \frac{\pi}{12}$$
$$x_{2} = \frac{\pi n}{6} - \frac{\pi}{12}$$

Быстрый ответ

     pi
x1 = --
     12

$$x_{1} = \frac{\pi}{12}$$

     pi
x2 = --
     4 

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

Сумма и произведение корней

сумма

    pi   pi
0 + -- + --
    12   4 

$$\left(0 + \frac{\pi}{12}\right) + \frac{\pi}{4}$$

=

pi
--
3 

$$\frac{\pi}{3}$$

произведение

  pi pi
1*--*--
  12 4 

$$\frac{\pi}{4} \cdot 1 \frac{\pi}{12}$$

=

  2
pi 
---
 48

$$\frac{\pi^{2}}{48}$$

Численный ответ

x1 = 68.329640215578

x2 = 6.02138591938044

x3 = -87.7027949127151

x4 = 3.92699081698724

x5 = -43.720497762458

x6 = 100.269165527074

x7 = -40.0553063332699

x8 = -96.0803753222878

x9 = 96.0803753222878

x10 = 66.2352451131848

x11 = 10.2101761241668

x12 = 22.2529479629277

x13 = -35.8665161284835

x14 = 32.2013246992954

x15 = -37.9609112308767

x16 = 24.3473430653209

x17 = -62.0464549083984

x18 = -89.7971900151083

x19 = 32.7249234748937

x20 = 0.261799387799149

x21 = 74.0892267471593

x22 = 46.3384916404494

x23 = -28.012534494509

x24 = -69.9004365423729

x25 = -55.7632696012188

x26 = 84.037603483527

x27 = 54.1924732744239

x28 = 44.2440965380563

x29 = 90.3207887907066

x30 = -45.8148928648512

x31 = 78.2780169519457

x32 = 47.9092879672443

x33 = 98.174770424681

x34 = 91.3679863419031

x35 = -47.9092879672443

x36 = 28.012534494509

x37 = -1.83259571459405

x38 = -91.8915851175014

x39 = -67.8060414399797

x40 = -13.8753675533549

x41 = -33.7721210260903

x42 = -18.0641577581413

x43 = -31.6777259236971

x44 = 76.1836218495525

x45 = 64.1408500107916

x46 = -97.6511716490827

x47 = -99.7455667514759

x48 = 56.2868683768171

x49 = 52.0980781720307

x50 = -30.6305283725005

x51 = -77.7544181763474

x52 = -57.857664703612

x53 = 12.30457122656

x54 = -40.5789051088682

x55 = 88.2263936883134

x56 = -3.92699081698724

x57 = 81.9432083811338

x58 = 86.1319985859202

x59 = -32.2013246992954

x60 = 89.7971900151083

x61 = -71.9948316447661

x62 = 8.11578102177363

x63 = 69.9004365423729

x64 = 80.3724120543389

x65 = 93.9859802198946

x66 = -9.68657734856853

x67 = 42.1497014356631

x68 = -15.9697626557481

x69 = 59.9520598060052

x70 = 30.1069295969022

x71 = -93.9859802198946

x72 = -61.5228561328001

x73 = -50.0036830696375

x74 = -79.8488132787406

x75 = -11.7809724509617

x76 = 62.0464549083984

x77 = 71.9948316447661

x78 = -53.6688744988256

x79 = -52.0980781720307

x80 = 2.87979326579064

x81 = -25.9181393921158

x82 = 18.0641577581413

x83 = -75.6600230739542

x84 = -74.6128255227576

x85 = 15.9697626557481

x86 = -59.9520598060052

x87 = 50.0036830696375

x88 = 37.9609112308767

x89 = -23.8237442897226

x90 = -65.7116463375865

x91 = 34.2957198016886

x92 = -74.0892267471593

x93 = 25.9181393921158

x94 = -84.037603483527

x95 = -21.7293491873294

x96 = 40.0553063332699

x97 = -81.9432083811338

x98 = 20.1585528605345

x99 = -6.02138591938044

График