9cosx-9=0 (уравнение)

Найду корень уравнения: 9cosx-9=0

Вы ввели

9*cos(x) - 9 = 0

$$9 \cos{\left(x \right)} - 9 = 0$$

Подробное решение

Дано уравнение
$$9 \cos{\left(x \right)} - 9 = 0$$
- это простейшее тригонометрическое ур-ние

Перенесём -9 в правую часть ур-ния

с изменением знака при -9

Получим:
$$9 \cos{\left(x \right)} - 9 + 9 = 9$$

Разделим обе части ур-ния на 9

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 = 6.28318528420851

x18 = -69.1150379045123

x19 = -37.6991121287155

x20 = 6.28318500093652

x21 = 25.1327416384075

x22 = -50.265482641087

x23 = 81.6814085860518

x24 = 37.6991120311338

x25 = 56.5486676011951

x26 = 43.9822974733639

x27 = -100.530964626003

x28 = -43.9822971745392

x29 = -31.4159260208155

x30 = -81.6814092565354

x31 = -43.9822967932182

x32 = 94.2477800892631

x33 = -6.28318555849548

x34 = -87.9645943586158

x35 = 50.2654824463392

x36 = -12.5663710889626

x37 = 87.9645938121814

x38 = 18.8495564031971

x39 = -69.1150386869085

x40 = 12.5663711301703

x41 = -37.6991113479743

x42 = 75.3982232188727

x43 = -31.4159267157965

x44 = -4.79511606158654e-7

x45 = 0.0

x46 = -62.831852673202

x47 = -12.5663703112531

x48 = 3.40772025642919e-7

x49 = 31.4159268459961

x50 = 12.5663710110881

x51 = -50.2654822863493

x52 = 43.9822966661001

x53 = -94.2477801171671

x54 = 12.5663704426592

x55 = -6.2831858160515

x56 = 62.8318527849002

x57 = -56.5486682426592

x58 = 62.8318535568358

x59 = 87.964594335905

x60 = -62.8318534787248

x61 = 69.1150379887504

x62 = 50.2654829439723

x63 = -94.2477794452815

x64 = 25.1327408328211

x65 = -87.9645947692094

x66 = 100.530964759815

x67 = 37.6991113348642

x68 = -25.1327407505866

x69 = 37.6991115173992

x70 = -94.2477797298079

x71 = 56.5486682809363

x72 = 50.2654821322586

x73 = -50.2654829667315

x74 = 87.9645946044253

x75 = -75.3982238741744

x76 = 81.6814084860076

x77 = 6.28318579821791

x78 = -43.9822976246252

x79 = 75.3982240031607

x80 = -18.8495563230046

x81 = -6.2831851275477

x82 = 100.530965157364

x83 = 69.115038794053

График