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

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

x2 = 6*pi

$$x_{2} = 6 \pi$$

Численный ответ

x1 = -75.3982238776703

x2 = 75.3982221706008

x3 = -18.8495563669393

x4 = 94.2477796093523

x5 = 18.8495565029992

x6 = 37.6991103849038

x7 = 37.6991128142893

x8 = 75.3982248314927

x9 = 56.5486684745659

x10 = 18.8495553483223

x11 = 37.6991144933771

x12 = 56.5486662460461

x13 = 56.548669225147

x14 = -8.08585122197531e-7

x15 = -94.2477810514324

x16 = -37.6991155544004

x17 = -18.8495571424909

x18 = 37.6991104721692

x19 = 18.8495547971151

x20 = -56.5486674541218

x21 = -56.548666555882

x22 = -37.6991104648259

x23 = 56.5486667913182

x24 = 18.8495556132183

x25 = -75.3982223117738

x26 = -37.6991110312352

x27 = -56.5486666369765

x28 = 94.2477804408697

x29 = 94.2477787012183

x30 = -56.5486692727618

x31 = -75.3982260019963

x32 = -75.3982229985229

x33 = -56.5486671092886

x34 = 37.6991120346156

x35 = 37.6991128846967

x36 = 94.2477810581664

x37 = -75.3982222122678

x38 = 1.49236450383454e-6

x39 = 75.3982240213672

x40 = -94.2477785834593

x41 = 18.8495549467782

x42 = -18.849555473224

x43 = -18.8495546973473

x44 = -18.8495558341898

x45 = -1.35506772311103e-6

x46 = -37.6991130291785

x47 = 56.5486667453654

x48 = 2.92197179834128e-6

x49 = 94.2477783856967

x50 = -94.2477794430271

x51 = 37.6991111586813

x52 = -56.5486690723182

x53 = 75.3982242556467

x54 = -75.3982247245508

x55 = 1.2213523817751e-6

x56 = -18.8495574586642

x57 = -37.699110402855

x58 = -56.5486683429152

x59 = -94.2477803143997

x60 = -37.6991127699674

x61 = 56.548665100694

x62 = 56.548665270306

x63 = 18.8495572325666

x64 = -37.6991133311021

x65 = -18.849555871711

x66 = 75.3982252330692

x67 = -75.3982252097189

x68 = 75.3982246512207

x69 = -94.2477809911003

x70 = 37.6991149564357

x71 = 56.5486675989004

x72 = 9.30134006720602e-7

x73 = -94.2477785852162

x74 = 18.8495543827121

x75 = -18.849554375974

x76 = 75.3982223930005

x77 = 56.5486691515392

x78 = 37.6991133718789

x79 = -75.3982246020911

x80 = 94.2477809633884

x81 = 0.0

x82 = -37.6991118772957

x83 = -56.5486662194246

x84 = -94.2477780840769

x85 = -1.43643093181333e-6

x86 = 75.3982231310034

x87 = 18.8495574413716

x88 = 94.2477781276767

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