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

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

Сумма и произведение корней

сумма

0 + 0 + 6*pi

$$\left(0 + 0\right) + 6 \pi$$

=

6*pi

$$6 \pi$$

произведение

1*0*6*pi

$$1 \cdot 0 \cdot 6 \pi$$

=

0

$$0$$

Численный ответ

x1 = -18.849554375974

x2 = 94.2477796093523

x3 = -56.5486662194246

x4 = -75.3982229985229

x5 = 37.6991128846967

x6 = 37.6991104721692

x7 = 18.8495574413716

x8 = 56.5486691515392

x9 = -94.2477785834593

x10 = -1.43643093181333e-6

x11 = 37.6991120346156

x12 = -1.35506772311103e-6

x13 = -18.849555473224

x14 = 2.92197179834128e-6

x15 = -56.5486666369765

x16 = 75.3982223930005

x17 = -56.548666555882

x18 = -94.2477785852162

x19 = 94.2477787012183

x20 = -75.3982247245508

x21 = -37.6991118772957

x22 = -94.2477810514324

x23 = 1.2213523817751e-6

x24 = -37.6991155544004

x25 = 75.3982246512207

x26 = -8.08585122197531e-7

x27 = -37.6991104648259

x28 = -18.8495574586642

x29 = -75.3982260019963

x30 = 18.8495543827121

x31 = 94.2477783856967

x32 = -37.699110402855

x33 = 37.6991149564357

x34 = 94.2477804408697

x35 = -37.6991127699674

x36 = 18.8495553483223

x37 = 75.3982252330692

x38 = -18.849555871711

x39 = -94.2477780840769

x40 = -56.5486692727618

x41 = 37.6991111586813

x42 = 75.3982240213672

x43 = 56.5486675989004

x44 = 75.3982231310034

x45 = -18.8495571424909

x46 = -75.3982223117738

x47 = 56.548669225147

x48 = 0.0

x49 = 94.2477809633884

x50 = 37.6991103849038

x51 = 18.8495547971151

x52 = 18.8495549467782

x53 = 56.548665270306

x54 = 1.49236450383454e-6

x55 = -37.6991130291785

x56 = -37.6991133311021

x57 = 18.8495565029992

x58 = -75.3982246020911

x59 = 94.2477810581664

x60 = 56.5486684745659

x61 = -56.5486674541218

x62 = 56.5486662460461

x63 = -75.3982252097189

x64 = 75.3982221706008

x65 = -75.3982238776703

x66 = -75.3982222122678

x67 = 18.8495556132183

x68 = 37.6991144933771

x69 = -56.5486690723182

x70 = 56.5486667913182

x71 = -56.5486671092886

x72 = 9.30134006720602e-7

x73 = 75.3982242556467

x74 = 37.6991128142893

x75 = -94.2477809911003

x76 = -94.2477794430271

x77 = 18.8495572325666

x78 = 56.5486667453654

x79 = 56.548665100694

x80 = -56.5486683429152

x81 = 94.2477781276767

x82 = -37.6991110312352

x83 = 75.3982248314927

x84 = -94.2477803143997

x85 = -18.8495558341898

x86 = 37.6991133718789

x87 = -18.8495563669393

x88 = -18.8495546973473

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