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
$$3 x = \pi n + \pi$$
$$3 x = \pi n$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$3$$
получим ответ:
$$x_{1} = \frac{\pi n}{3} + \frac{\pi}{3}$$
$$x_{2} = \frac{\pi n}{3}$$

Быстрый ответ

     pi
x1 = --
     3 

$$x_{1} = \frac{\pi}{3}$$

Сумма и произведение корней

сумма

    pi
0 + --
    3 

$$0 + \frac{\pi}{3}$$

=

pi
--
3 

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

произведение

  pi
1*--
  3 

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

=

pi
--
3 

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

Численный ответ

x1 = 84.8230015250443

x2 = -7.33038302030457

x3 = -49.2182850519149

x4 = -65.973445765171

x5 = -70.1622358204673

x6 = -68.0678407687851

x7 = -5.23598790794418

x8 = -24.0855436072883

x9 = 74.3510260729228

x10 = -15.7079632964021

x11 = -9.42477810882172

x12 = -89.0117914375586

x13 = 21.9911485851801

x14 = -97.3893724165565

x15 = 17.8023584945614

x16 = 82.7286063849234

x17 = 15.7079634213668

x18 = -82.7286069074292

x19 = -11.5191731827034

x20 = 36.6519141311518

x21 = 97.3893723442985

x22 = -53.4070752629576

x23 = -93.2005821937681

x24 = 65.9734457527543

x25 = 28.2743338652382

x26 = 72.2566310277214

x27 = -28.2743337333192

x28 = 11.5191732261809

x29 = 59.6902605755492

x30 = 32.463123974206

x31 = -51.3126801709688

x32 = -57.5958654038294

x33 = 99.4837675171026

x34 = 68.0678406256452

x35 = 40.8407043904405

x36 = 30.3687289136091

x37 = 26.1799388481654

x38 = -99.4837674953423

x39 = 34.5575190458158

x40 = -3.14159273948893

x41 = -72.2566308884953

x42 = -91.1061869787177

x43 = -76.4454210695477

x44 = -74.3510259705245

x45 = -26.1799386626996

x46 = 86.9173967892295

x47 = 38.7463092377642

x48 = -34.5575190560831

x49 = -59.6902604573636

x50 = 61.7846556513336

x51 = -78.5398161963125

x52 = 76.4454211314942

x53 = -61.7846554919628

x54 = -95.2949773207426

x55 = -21.9911485864683

x56 = 19.8967535532584

x57 = -80.6342113974683

x58 = 63.8790507130208

x59 = 9.42477808135176

x60 = -19.8967529903279

x61 = 95.294976948998

x62 = -32.4631239211685

x63 = -55.501470339224

x64 = 13.6135683335585

x65 = 55.5014703723413

x66 = 57.595865484629

x67 = 42.9350997066251

x68 = -1.04719735385243

x69 = -36.6519142867263

x70 = -47.1238898632468

x71 = 70.1622360266582

x72 = -17.8023583238223

x73 = -112.050138233058

x74 = -45.0294943910096

x75 = 53.4070752151879

x76 = 93.2005824359632

x77 = 7.33038281101878

x78 = 80.6342112833208

x79 = -30.3687288181742

x80 = 51.3126798911883

x81 = -38.7463098041192

x82 = 78.5398162009252

x83 = -13.6135682453022

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