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

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

Сумма и произведение корней

сумма

0 + 3*pi

$$0 + 3 \pi$$

=

3*pi

$$3 \pi$$

произведение

1*3*pi

$$1 \cdot 3 \pi$$

=

3*pi

$$3 \pi$$

Численный ответ

x1 = 47.1238885910376

x2 = 28.2743323982258

x3 = 28.2743304203258

x4 = -47.1238913434704

x5 = -103.672556179644

x6 = -9.42478044884868

x7 = -47.1238903314038

x8 = 28.2743338651733

x9 = -65.9734442370237

x10 = -9.42477898962262

x11 = 28.2743353277095

x12 = -84.8230001004278

x13 = 84.82300316301

x14 = -84.8230028759433

x15 = -84.8230012105749

x16 = -28.2743328840357

x17 = 9.42477828364719

x18 = -47.1238882805255

x19 = -9.42477658006982

x20 = 47.1238910361097

x21 = 47.1238898180831

x22 = 9.42477857411892

x23 = 47.1238897836275

x24 = 84.8230029651094

x25 = 28.2743324300573

x26 = 47.1238882655668

x27 = 9.42477904486572

x28 = 65.9734449275366

x29 = 65.9734466656459

x30 = -84.8230015302339

x31 = 65.9734443589411

x32 = 65.9734457530057

x33 = 65.9734496550071

x34 = -84.8230014829494

x35 = -28.2743342852867

x36 = -84.8230021042216

x37 = 84.8230010300176

x38 = 84.8230005314505

x39 = -216.769897336347

x40 = -65.9734471669578

x41 = 9.42477909729197

x42 = -47.1238906645642

x43 = -9.4247794819084

x44 = -65.9734457649013

x45 = 28.2743326778891

x46 = 9.42477950690576

x47 = -28.2743337041057

x48 = 47.1238902640918

x49 = -47.1238892339559

x50 = 9.42477666029867

x51 = 28.2743352495238

x52 = 84.8230013509188

x53 = 65.9734472216308

x54 = -28.2743328502299

x55 = 65.9734442942041

x56 = -103.672561360559

x57 = -84.8230031826845

x58 = 9.42477644878639

x59 = -47.1238870896323

x60 = 47.123891348278

x61 = -9.42477726195834

x62 = 28.2743347048405

x63 = -65.9734470685728

x64 = 103.672556203947

x65 = 84.823000552695

x66 = -28.2743352595136

x67 = -47.1238901244433

x68 = -65.9734448054309

x69 = 103.672556103604

x70 = -28.2743310539003

x71 = -9.42477649339056

x72 = 65.9734469290305

x73 = -47.1238885000614

x74 = -84.8230004308799

x75 = -47.1238909371531

x76 = -9.424778905987

x77 = -28.2743353334451

x78 = -103.672556133526

x79 = -65.9734441237693

x80 = -28.2743345778791

x81 = 47.1238893703748

x82 = -9.42477813943337

x83 = -65.9734465446611

x84 = -28.274332356029

x85 = 65.973449200012

x86 = 103.672560042967

x87 = -65.973444487036

x88 = 28.2743329655993

x89 = 23495.9714577684

x90 = 84.8230022399184

x91 = 9.42477739402688

x92 = 84.8230001090646

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