cos6x=1 (уравнение)

Найду корень уравнения: cos6x=1

Вы ввели

cos(6*x) = 1

$$\cos{\left(6 x \right)} = 1$$

Подробное решение

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

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

     pi
x2 = --
     3 

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

Численный ответ

x1 = 10.4719754514552

x2 = 59.6902602103008

x3 = 70.1622360218137

x4 = -17.8023583237749

x5 = 12.566370486226

x6 = 54.4542725942726

x7 = -81.6814090352758

x8 = -70.1622358532669

x9 = 63.8790506955489

x10 = 50.2654824464452

x11 = -52.3598773534304

x12 = 61.7846555856111

x13 = 87.9645943339958

x14 = 32.463124022232

x15 = 56.5486679087207

x16 = 76.445421167341

x17 = -6.28318536172932

x18 = -99.4837673664303

x19 = 92.153384609279

x20 = -46.0766921948394

x21 = -50.2654824528405

x22 = 21.9911485850825

x23 = -61.7846554917911

x24 = -92.1533844285198

x25 = 94.2477796093541

x26 = -33.5103216848946

x27 = 96.3421746575137

x28 = -28.2743339027943

x29 = -79.587013962129

x30 = -13.6135682324625

x31 = -48.1710872785046

x32 = 26.1799388472337

x33 = 72.2566310277355

x34 = 68.0678406435528

x35 = 78.5398164276763

x36 = -57.5958653860056

x37 = -59.6902604556648

x38 = 39.7935070144417

x39 = -26.1799387042774

x40 = -15.7079632956456

x41 = -71.2094334160924

x42 = 48.1710874341111

x43 = 41.8879021182991

x44 = 8.37758034488241

x45 = 15.7079631676307

x46 = -83.7758040749281

x47 = 28.2743338654616

x48 = 100.530964959912

x49 = -55.5014702493934

x50 = 4.18879026129896

x51 = -21.9911485865686

x52 = -24.0855436159154

x53 = 6.2831852847685

x54 = 90.0589892608867

x55 = -90.0589893540864

x56 = 37.699111685071

x57 = 34.5575193908685

x58 = -87.9645943606119

x59 = 85.8701992723906

x60 = 74.351026078903

x61 = 19.896753540642

x62 = 83.7758041420923

x63 = -2.09439503742649

x64 = -11.5191731177358

x65 = -37.6991118757886

x66 = 30.3687289225719

x67 = -65.9734457660819

x68 = -35.6047168094363

x69 = -39.7935069081029

x70 = 65.973445751897

x71 = -94.2477795706448

x72 = 0.0

x73 = 52.3598775005845

x74 = -72.2566310094027

x75 = 98.4365697412614

x76 = -77.4926188103359

x77 = 43.9822971689772

x78 = -43.9822971750521

x79 = -4.18879013064742

x80 = 83.7758041555675

x81 = -68.0678407742199

x82 = 17.8023584422991

x83 = -458.672527220906

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