cos3x=1 (уравнение)

Найду корень уравнения: cos3x=1

Вы ввели

cos(3*x) = 1

$$\cos{\left(3 x \right)} = 1$$

Подробное решение

Дано уравнение
$$\cos{\left(3 x \right)} = 1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$3 x = \pi n + \operatorname{acos}{\left(1 \right)}$$
$$3 x = \pi n - \pi + \operatorname{acos}{\left(1 \right)}$$
Или
$$3 x = \pi n$$
$$3 x = \pi n - \pi$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$3$$
получим ответ:
$$x_{1} = \frac{\pi n}{3}$$
$$x_{2} = \frac{\pi n}{3} - \frac{\pi}{3}$$

Сумма и произведение корней

сумма

        2*pi
0 + 0 + ----
         3  

$$\left(0 + 0\right) + \frac{2 \pi}{3}$$

=

2*pi
----
 3  

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

произведение

    2*pi
1*0*----
     3  

$$1 \cdot 0 \cdot \frac{2 \pi}{3}$$

=

0

$$0$$

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

     2*pi
x2 = ----
      3  

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

Численный ответ

x1 = -83.7758040750549

x2 = -60.7374583801782

x3 = 10.4719753957034

x4 = 46.076691966571

x5 = -25.1327413022544

x6 = 50.2654824463613

x7 = 31.4159266487811

x8 = -77.4926189173344

x9 = 43.9822971693627

x10 = 52.3598774932141

x11 = 6.28318528432449

x12 = 37.6991113434848

x13 = -23.0383458748855

x14 = 90.0589892608483

x15 = -94.2477794662643

x16 = 73.3038284231128

x17 = -12.5663704869723

x18 = 33.5103217994214

x19 = 29.3215313536198

x20 = 98.4365697102782

x21 = 79.5870140598991

x22 = -81.6814090376256

x23 = 20.943951173337

x24 = 98.4365698045197

x25 = -92.1533843995496

x26 = -71.2094336231345

x27 = 85.8701992926441

x28 = -4.18879008400713

x29 = 77.4926189449124

x30 = 161.26842260871

x31 = 39.7935070730078

x32 = -73.3038287459741

x33 = 64.9262482454786

x34 = 8.37758033410453

x35 = 54.4542725528033

x36 = -27.2271364801679

x37 = -33.5103217610131

x38 = 58.6430627071515

x39 = 62.8318529572331

x40 = 56.5486676233132

x41 = -441575121.501282

x42 = 37.6991119985219

x43 = -29.3215315957413

x44 = -96.3421745469196

x45 = -67.0206429069494

x46 = -100.530964767287

x47 = -35.604716824613

x48 = -37.6991118769598

x49 = -87.964594359041

x50 = -41.8879015909008

x51 = -56.548667625889

x52 = -85.8701992330716

x53 = 94.2477796093527

x54 = -8.37758024222806

x55 = 83.7758042295396

x56 = 4.18879026156543

x57 = -69.115038422181

x58 = 833.569250843322

x59 = -79.5870139829524

x60 = -69.1150389029232

x61 = 92.1533846197794

x62 = -14.6607657359666

x63 = -35.6047172724316

x64 = -58.6430628407171

x65 = -6.28318515591421

x66 = 14.6607655553299

x67 = -20.9439509761532

x68 = -2.09439502690814

x69 = 87.9645943355056

x70 = -90.0589893499645

x71 = 12.5663704684363

x72 = 60.7374578111775

x73 = -46.0766921879046

x74 = -10.4719753473561

x75 = -52.3598773942745

x76 = -75.3982238398266

x77 = 18.8495558248099

x78 = 96.3421746527392

x79 = -43.9822971746469

x80 = 35.6047169091797

x81 = 81.6814091524463

x82 = -16.755160961199

x83 = 75.3982237804204

x84 = 0.0

x85 = -48.1710872415186

x86 = -50.2654823108466

x87 = 48.1710874363538

x88 = 41.8879021332297

x89 = 100.530964778649

x90 = -54.4542724952377

x91 = -39.7935069082666

x92 = -98.4365696440843

x93 = 16.7551606647126

x94 = -31.4159266859544

График