2cosx-2=0 (уравнение)

Найду корень уравнения: 2cosx-2=0

Вы ввели

2*cos(x) - 2 = 0

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

Подробное решение

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

Перенесём -2 в правую часть ур-ния

с изменением знака при -2

Получим:
$$2 \cos{\left(x \right)} - 2 + 2 = 2$$

Разделим обе части ур-ния на 2

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 = 31.4159260648825

x2 = 43.9822971694647

x3 = 94.2477792651059

x4 = -18.8495555173448

x5 = 56.5486680806249

x6 = -75.3982231720141

x7 = -25.1327415297174

x8 = -56.5486674685864

x9 = -31.4159260507536

x10 = 81.6814091897036

x11 = -87.964593928489

x12 = -37.6991118772631

x13 = -81.6814084945807

x14 = 18.8495556275525

x15 = -81.6814090382277

x16 = 94.2477796093523

x17 = 6.28318626747926

x18 = -4.79511606158654e-7

x19 = 6.28318528420851

x20 = -69.1150379045123

x21 = -37.6991121287155

x22 = -18.8495552124105

x23 = 6.28318500093652

x24 = 25.1327416384075

x25 = -50.265482641087

x26 = 81.6814085860518

x27 = 37.6991120311338

x28 = 56.5486676011951

x29 = 43.9822974733639

x30 = -100.530964626003

x31 = -43.9822971745392

x32 = -31.4159260208155

x33 = -81.6814092565354

x34 = -43.9822967932182

x35 = 94.2477800892631

x36 = -6.28318555849548

x37 = -87.9645943586158

x38 = 50.2654824463392

x39 = 56.5486668532011

x40 = -12.5663710889626

x41 = 87.9645938121814

x42 = 18.8495564031971

x43 = -69.1150386869085

x44 = 12.5663711301703

x45 = -37.6991113479743

x46 = 75.3982232188727

x47 = -31.4159267157965

x48 = 0.0

x49 = -62.831852673202

x50 = -12.5663703112531

x51 = 31.4159268459961

x52 = 3.40772025642919e-7

x53 = 12.5663710110881

x54 = -50.2654822863493

x55 = 43.9822966661001

x56 = -94.2477801171671

x57 = 12.5663704426592

x58 = -6.2831858160515

x59 = 62.8318527849002

x60 = -56.5486682426592

x61 = 62.8318535568358

x62 = 87.964594335905

x63 = -62.8318534787248

x64 = 69.1150379887504

x65 = 50.2654829439723

x66 = -94.2477794452815

x67 = -75.3982231045728

x68 = 25.1327408328211

x69 = -87.9645947692094

x70 = 100.530964759815

x71 = 37.6991113348642

x72 = -25.1327407505866

x73 = 37.6991115173992

x74 = -94.2477797298079

x75 = 56.5486682809363

x76 = 50.2654821322586

x77 = -50.2654829667315

x78 = 87.9645946044253

x79 = -75.3982238741744

x80 = 81.6814084860076

x81 = 6.28318579821791

x82 = -43.9822976246252

x83 = 75.3982240031607

x84 = -18.8495563230046

x85 = -6.2831851275477

x86 = 100.530965157364

x87 = 69.115038794053

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