Cos2x-1=0 (уравнение)

Найду корень уравнения: Cos2x-1=0

Вы ввели

cos(2*x) - 1 = 0

$$\cos{\left(2 x \right)} - 1 = 0$$

Подробное решение

Дано уравнение
$$\cos{\left(2 x \right)} - 1 = 0$$
- это простейшее тригонометрическое ур-ние

Перенесём -1 в правую часть ур-ния

с изменением знака при -1

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

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

x2 = pi

$$x_{2} = \pi$$

Сумма и произведение корней

сумма

0 + 0 + pi

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

=

pi

$$\pi$$

произведение

1*0*pi

$$1 \cdot 0 \pi$$

=

0

$$0$$

Численный ответ

x1 = -91.1061872003049

x2 = -6.28318513794069

x3 = -94.2477794529919

x4 = -50.2654822953391

x5 = -34.5575189701076

x6 = -47.1238900492539

x7 = 100.530964766599

x8 = -69.1150386737158

x9 = -56.5486675191652

x10 = 84.8230010166547

x11 = 53.4070753627408

x12 = -78.5398160958028

x13 = 97.3893727097471

x14 = 65.9734457528975

x15 = 9.42477821024198

x16 = 50.2654824463473

x17 = 9.42477859080277

x18 = -31.4159267959754

x19 = 28.2743338652012

x20 = 40.8407042560881

x21 = -3.14159289677385

x22 = 25.1327414478072

x23 = -91.106187201329

x24 = -28.2743337166085

x25 = 31.4159271479423

x26 = -9.42477812668337

x27 = 56.5486676091327

x28 = -15.7079632965264

x29 = 40.840703919946

x30 = 12.5663704518704

x31 = -65.9734457650176

x32 = 97.3893725148693

x33 = 62.8318524523063

x34 = 47.123889589354

x35 = 72.256631027719

x36 = -87.9645943587732

x37 = -25.132741473063

x38 = -6371388.6625218

x39 = -43.9822971745789

x40 = -84.8230018263493

x41 = 3.14159287686128

x42 = -34.5575189426108

x43 = 31.4159267865366

x44 = -21.9911485864515

x45 = 78.5398161878405

x46 = 25.1327410188866

x47 = -69.1150386253436

x48 = 18.8495556796107

x49 = -62.8318528379059

x50 = -18.8495561207399

x51 = -12.5663703661411

x52 = -18.8495556944209

x53 = -81.6814090380061

x54 = -1734.15914475848

x55 = -84.82300141007

x56 = 62.8318528326557

x57 = 37.6991120192083

x58 = -25.132741632083

x59 = -40.8407042660168

x60 = 21.9911485851964

x61 = -59.6902604576401

x62 = -47.123890151099

x63 = 84.8230014093114

x64 = 94.2477796093525

x65 = 15.7079634406648

x66 = 47.123890018392

x67 = -72.2566308741333

x68 = -40.8407046898283

x69 = 43.982297169427

x70 = 81.6814091761104

x71 = 91.1061871583643

x72 = -62.8318532583801

x73 = 34.5575190304759

x74 = -37.6991118771514

x75 = 3.14159244884412

x76 = -100.530964672522

x77 = 91.1061867314459

x78 = 75.3982239388525

x79 = 6.28318528425126

x80 = 0.0

x81 = -97.3893724403711

x82 = -75.3982238620294

x83 = -106.814150357553

x84 = -3.14159311568248

x85 = 69.1150381602162

x86 = -12.5663700417108

x87 = 53.4070756765307

x88 = -53.4070752836338

x89 = 75.3982241944528

x90 = -31.4159267051849

x91 = 69.1150385885879

x92 = 59.6902605976901

x93 = 18.8495554002244

x94 = 87.9645943357576

График