cos(x)-1=0 (уравнение)

Найду корень уравнения: cos(x)-1=0

Вы ввели

cos(x) - 1 = 0

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

Подробное решение

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

Перенесём -1 в правую часть ур-ния

с изменением знака при -1

Получим:
$$\cos{\left(x \right)} - 1 + 1 = 1$$
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(1 \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(1 \right)}$$
Или
$$x = \pi n$$
$$x = \pi n - \pi$$
, где n - любое целое число

Сумма и произведение корней

сумма

0 + 0 + 2*pi

$$\left(0 + 0\right) + 2 \pi$$

=

2*pi

$$2 \pi$$

произведение

1*0*2*pi

$$1 \cdot 0 \cdot 2 \pi$$

=

0

$$0$$

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

x2 = 2*pi

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

Численный ответ

x1 = -12.5663703112531

x2 = -43.9822976246252

x3 = 56.5486668532011

x4 = 56.5486682809363

x5 = 87.964594335905

x6 = 6.28318579821791

x7 = 12.5663704426592

x8 = 12.5663710110881

x9 = -18.8495563230046

x10 = 87.9645938121814

x11 = 50.2654821322586

x12 = 37.6991113348642

x13 = -62.831852673202

x14 = 62.8318527849002

x15 = -87.964593928489

x16 = -43.9822971745392

x17 = 6.28318626747926

x18 = -31.4159267157965

x19 = -25.1327415297174

x20 = 37.6991120311338

x21 = -50.265482641087

x22 = -75.3982238741744

x23 = -6.28318555849548

x24 = 100.530964759815

x25 = 94.2477800892631

x26 = 81.6814084860076

x27 = -31.4159260208155

x28 = 81.6814085860518

x29 = -43.9822967932182

x30 = 50.2654829439723

x31 = 100.530965157364

x32 = -6.2831858160515

x33 = -81.6814075578313

x34 = -56.5486674685864

x35 = -94.2477794452815

x36 = 94.2477796093523

x37 = -69.1150379045123

x38 = 37.6991115173992

x39 = 75.3982232188727

x40 = 50.2654824463392

x41 = 6.28318500093652

x42 = -75.3982231720141

x43 = -94.2477801171671

x44 = -37.6991121287155

x45 = 12.5663711301703

x46 = 25.1327408328211

x47 = -94.2477797298079

x48 = -50.2654822863493

x49 = -62.8318534787248

x50 = -4.79511606158654e-7

x51 = -18.8495552124105

x52 = 0.0

x53 = 18.8495564031971

x54 = -18.8495555173448

x55 = -100.530964626003

x56 = 43.9822966661001

x57 = -56.5486682426592

x58 = 62.8318535568358

x59 = 87.9645946044253

x60 = -31.4159260507536

x61 = 56.5486680806249

x62 = -81.6814092565354

x63 = -81.6814084945807

x64 = 43.9822974733639

x65 = -87.9645947692094

x66 = -37.6991113479743

x67 = 31.4159260648825

x68 = -50.2654829667315

x69 = 43.9822971694647

x70 = -25.1327407505866

x71 = -75.3982231045728

x72 = -6.2831851275477

x73 = 3.40772025642919e-7

x74 = -69.1150386869085

x75 = 69.115038794053

x76 = 81.6814091897036

x77 = 6.28318528420851

x78 = -87.9645943586158

x79 = 69.1150379887504

x80 = -12.5663710889626

x81 = -81.6814090382277

x82 = 31.4159268459961

x83 = -37.6991118772631

x84 = 25.1327416384075

x85 = 18.8495556275525

x86 = 75.3982240031607

x87 = 56.5486676011951

x88 = 94.2477792651059

График