cos(x/2)=1 (уравнение)

Найду корень уравнения: cos(x/2)=1

Вы ввели

   /x\    
cos|-| = 1
   \2/    

$$\cos{\left(\frac{x}{2} \right)} = 1$$

Подробное решение

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

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

x2 = 4*pi

$$x_{2} = 4 \pi$$

Сумма и произведение корней

сумма

0 + 0 + 4*pi

$$\left(0 + 0\right) + 4 \pi$$

=

4*pi

$$4 \pi$$

произведение

1*0*4*pi

$$1 \cdot 0 \cdot 4 \pi$$

=

0

$$0$$

Численный ответ

x1 = -75.398224618165

x2 = 87.9645943359415

x3 = -62.8318526379222

x4 = 100.530964758156

x5 = 50.2654832362872

x6 = 25.1327416777796

x7 = -87.9645934511713

x8 = -87.9645934903961

x9 = 62.8318531970184

x10 = -50.265481935943

x11 = 25.1327427229237

x12 = 62.8318527737309

x13 = -100.530963933814

x14 = -9.20147750307351e-7

x15 = 12.5663704404135

x16 = -2450.4422691113

x17 = -50.2654831290744

x18 = 7.856665190876e-7

x19 = -37.6991109019735

x20 = -50.2654829362526

x21 = -791.681347222187

x22 = 12.5663696903306

x23 = 37.6991111844838

x24 = 75.3982240185352

x25 = 100.530963999089

x26 = -12.5663711704395

x27 = 37.699112034073

x28 = -12.5663716390742

x29 = 75.3982234996238

x30 = 12.5663701654734

x31 = 12.5663716216992

x32 = 50.2654816836948

x33 = -100.530964897478

x34 = -25.1327422115415

x35 = 87.964593548137

x36 = -75.3982226734831

x37 = -50.2654834520414

x38 = -87.9645950762365

x39 = -50.2654815299205

x40 = -113.097333611656

x41 = -37.6991110758133

x42 = -25.1327429452907

x43 = -62.8318535180004

x44 = 62.8318541035118

x45 = -339.292004463459

x46 = 87.9645951697672

x47 = 75.3982242010893

x48 = 25.1327402133162

x49 = 50.2654816113039

x50 = -37.6991126992556

x51 = -12.5663706941362

x52 = -62.8318520510992

x53 = 50.2654824463372

x54 = 75.3982226607454

x55 = 25.1327398318424

x56 = -75.3982238771266

x57 = -62.8318542584121

x58 = 25.1327422523855

x59 = -25.1327401961945

x60 = 12.5663724644809

x61 = -50.2654822841315

x62 = 50.2654833855111

x63 = -25.1327409922366

x64 = 100.530965273463

x65 = -25.1327415428233

x66 = -12.5663702980387

x67 = 37.6991127786276

x68 = -87.9645952061008

x69 = -25.1327406696083

x70 = -62.831851347466

x71 = -12.5663696273954

x72 = 37.6991123150382

x73 = -37.6991118772906

x74 = 75.3982231443299

x75 = 8.5940846942539e-7

x76 = 62.8318536450421

x77 = 25.1327407976605

x78 = 87.9645933670472

x79 = -87.9645943585769

x80 = -37.6991125894353

x81 = 0.0

x82 = 75.3982246787105

x83 = -100.53096461474

x84 = 100.530964414577

x85 = -62.8318540899534

x86 = 87.9645950596493

x87 = 37.6991108423748

x88 = -7.64143136364703e-7

x89 = 12.566371289085

x90 = 62.8318520947719

x91 = 100.530964589585

x92 = -75.3982230244771

x93 = -75.3982240789539

x94 = 37.6991112800661

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