1-cos(x)=0 (уравнение)

Найду корень уравнения: 1-cos(x)=0

Вы ввели

1 - cos(x) = 0

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

Подробное решение

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

Перенесём 1 в правую часть ур-ния

с изменением знака при 1

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

Разделим обе части ур-ния на -1

Ур-ние превратится в
$$\cos{\left(x \right)} = 1$$
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

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

x2 = 2*pi

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

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

$$0$$

Численный ответ

x1 = 25.1327416384075

x2 = 12.5663704426592

x3 = 43.9822966661001

x4 = 50.2654821322586

x5 = -37.6991121287155

x6 = -4.79511606158654e-7

x7 = -43.9822967932182

x8 = -31.4159260507536

x9 = -81.6814090382277

x10 = 75.3982232188727

x11 = 56.5486680806249

x12 = 81.6814091897036

x13 = -18.8495555173448

x14 = -6.2831851275477

x15 = -56.5486682426592

x16 = 50.2654824463392

x17 = -62.8318534787248

x18 = -81.6814075578313

x19 = -25.1327407505866

x20 = 100.530964759815

x21 = -94.2477797298079

x22 = -43.9822976246252

x23 = 31.4159268459961

x24 = 81.6814084860076

x25 = -87.9645943586158

x26 = -12.5663710889626

x27 = 62.8318527849002

x28 = 37.6991120311338

x29 = 56.5486682809363

x30 = -69.1150386869085

x31 = 69.115038794053

x32 = 12.5663711301703

x33 = -18.8495552124105

x34 = -81.6814084945807

x35 = -50.2654822863493

x36 = -43.9822971745392

x37 = 87.964594335905

x38 = 56.5486676011951

x39 = 75.3982240031607

x40 = 87.9645938121814

x41 = -37.6991113479743

x42 = 31.4159260648825

x43 = 37.6991115173992

x44 = -12.5663703112531

x45 = -56.5486674685864

x46 = -75.3982238741744

x47 = 18.8495564031971

x48 = -50.265482641087

x49 = 37.6991113348642

x50 = -75.3982231045728

x51 = 81.6814085860518

x52 = -94.2477794452815

x53 = -18.8495563230046

x54 = 12.5663710110881

x55 = -100.530964626003

x56 = 6.28318626747926

x57 = 94.2477792651059

x58 = 62.8318535568358

x59 = -31.4159267157965

x60 = 25.1327408328211

x61 = 18.8495556275525

x62 = -31.4159260208155

x63 = -87.9645947692094

x64 = 56.5486668532011

x65 = 50.2654829439723

x66 = 6.28318579821791

x67 = 3.40772025642919e-7

x68 = -94.2477801171671

x69 = 43.9822974733639

x70 = -81.6814092565354

x71 = -25.1327415297174

x72 = 94.2477796093523

x73 = 43.9822971694647

x74 = -37.6991118772631

x75 = -6.28318555849548

x76 = 0.0

x77 = -75.3982231720141

x78 = 87.9645946044253

x79 = -50.2654829667315

x80 = -87.964593928489

x81 = 6.28318500093652

x82 = 69.1150379887504

x83 = -69.1150379045123

x84 = 94.2477800892631

x85 = -62.831852673202

x86 = -6.2831858160515

x87 = 6.28318528420851

x88 = 100.530965157364

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