cos (x/3)=−1 (уравнение)

Найду корень уравнения: cos (x/3)=−1

Вы ввели

   /x\     
cos|-| = -1
   \3/     

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

Подробное решение

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

Быстрый ответ

x1 = 3*pi

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

Численный ответ

x1 = -65.9734471669578

x2 = 65.9734469290305

x3 = 9.42477950690576

x4 = 47.1238885910376

x5 = 65.9734472216308

x6 = -65.9734442370237

x7 = 103.672560042967

x8 = -28.2743352595136

x9 = 65.9734466656459

x10 = -28.2743328502299

x11 = 9.42477666029867

x12 = -65.9734470685728

x13 = -47.1238882805255

x14 = -65.9734457649013

x15 = 47.1238893703748

x16 = 65.9734442942041

x17 = 84.8230013509188

x18 = 28.2743352495238

x19 = -65.9734448054309

x20 = -103.672556179644

x21 = -9.42477726195834

x22 = 103.672556103604

x23 = -28.2743345778791

x24 = -28.2743353334451

x25 = -28.2743342852867

x26 = 9.42477857411892

x27 = -47.1238913434704

x28 = 28.2743304203258

x29 = -9.42477813943337

x30 = -84.8230012105749

x31 = 103.672556203947

x32 = 47.1238898180831

x33 = 9.42477904486572

x34 = -65.973444487036

x35 = -84.8230004308799

x36 = -9.42477898962262

x37 = 9.42477739402688

x38 = -47.1238901244433

x39 = 28.2743338651733

x40 = -103.672556133526

x41 = 47.1238897836275

x42 = -103.672561360559

x43 = 28.2743329655993

x44 = 84.8230001090646

x45 = -47.1238906645642

x46 = -47.1238885000614

x47 = -9.42477658006982

x48 = -84.8230028759433

x49 = -28.2743328840357

x50 = -84.8230031826845

x51 = -9.42478044884868

x52 = 28.2743347048405

x53 = -65.9734441237693

x54 = -65.9734465446611

x55 = 65.9734496550071

x56 = 47.1238910361097

x57 = 28.2743353277095

x58 = -216.769897336347

x59 = 84.82300316301

x60 = 65.973449200012

x61 = -9.42477649339056

x62 = 23495.9714577684

x63 = -84.8230014829494

x64 = -28.2743310539003

x65 = 9.42477644878639

x66 = 65.9734457530057

x67 = -9.424778905987

x68 = -47.1238909371531

x69 = 28.2743324300573

x70 = -47.1238903314038

x71 = -47.1238892339559

x72 = -84.8230021042216

x73 = -84.8230015302339

x74 = 28.2743326778891

x75 = -84.8230001004278

x76 = 9.42477909729197

x77 = -47.1238870896323

x78 = 9.42477828364719

x79 = 84.8230029651094

x80 = 47.1238882655668

x81 = 84.8230022399184

x82 = 84.8230010300176

x83 = 84.823000552695

x84 = 65.9734443589411

x85 = -28.2743337041057

x86 = 65.9734449275366

x87 = 47.123891348278

x88 = -9.4247794819084

x89 = 84.8230005314505

x90 = -28.274332356029

x91 = 47.1238902640918

x92 = 28.2743323982258

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