cos(6x)=1 (уравнение)

Найду корень уравнения: cos(6x)=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 

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

Сумма и произведение корней

сумма

        pi
0 + 0 + --
        3 

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

=

pi
--
3 

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

произведение

    pi
1*0*--
    3 

$$1 \cdot 0 \frac{\pi}{3}$$

=

0

$$0$$

Численный ответ

x1 = -70.1622358532669

x2 = -72.2566310094027

x3 = 83.7758041420923

x4 = 61.7846555856111

x5 = 43.9822971689772

x6 = -99.4837673664303

x7 = 63.8790506955489

x8 = 4.18879026129896

x9 = 59.6902602103008

x10 = -13.6135682324625

x11 = -50.2654824528405

x12 = -458.672527220906

x13 = -43.9822971750521

x14 = -55.5014702493934

x15 = 78.5398164276763

x16 = 30.3687289225719

x17 = 26.1799388472337

x18 = 96.3421746575137

x19 = 87.9645943339958

x20 = 48.1710874341111

x21 = -71.2094334160924

x22 = -21.9911485865686

x23 = 17.8023584422991

x24 = -11.5191731177358

x25 = -81.6814090352758

x26 = -87.9645943606119

x27 = 34.5575193908685

x28 = 19.896753540642

x29 = 72.2566310277355

x30 = -57.5958653860056

x31 = -2.09439503742649

x32 = -77.4926188103359

x33 = -35.6047168094363

x34 = 92.153384609279

x35 = 68.0678406435528

x36 = -83.7758040749281

x37 = -65.9734457660819

x38 = -24.0855436159154

x39 = 76.445421167341

x40 = -61.7846554917911

x41 = 74.351026078903

x42 = -15.7079632956456

x43 = 32.463124022232

x44 = -4.18879013064742

x45 = -48.1710872785046

x46 = -79.587013962129

x47 = 28.2743338654616

x48 = -37.6991118757886

x49 = 10.4719754514552

x50 = 21.9911485850825

x51 = 94.2477796093541

x52 = -26.1799387042774

x53 = 65.973445751897

x54 = 85.8701992723906

x55 = 54.4542725942726

x56 = -94.2477795706448

x57 = -28.2743339027943

x58 = -17.8023583237749

x59 = -39.7935069081029

x60 = 100.530964959912

x61 = -46.0766921948394

x62 = 37.699111685071

x63 = 70.1622360218137

x64 = 39.7935070144417

x65 = 98.4365697412614

x66 = -52.3598773534304

x67 = -59.6902604556648

x68 = 56.5486679087207

x69 = 0.0

x70 = -92.1533844285198

x71 = 41.8879021182991

x72 = 6.2831852847685

x73 = 12.566370486226

x74 = -33.5103216848946

x75 = 15.7079631676307

x76 = 83.7758041555675

x77 = -68.0678407742199

x78 = 50.2654824464452

x79 = 90.0589892608867

x80 = 8.37758034488241

x81 = -6.28318536172932

x82 = -90.0589893540864

x83 = 52.3598775005845

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