cos(x)=-1/8 (уравнение)

Найду корень уравнения: cos(x)=-1/8

Вы ввели

cos(x) = -1/8

$$\cos{\left(x \right)} = - \frac{1}{8}$$

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = - \frac{1}{8}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(- \frac{1}{8} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{1}{8} \right)}$$
Или
$$x = \pi n + \operatorname{acos}{\left(- \frac{1}{8} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{1}{8} \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = -acos(-1/8) + 2*pi

$$x_{1} = - \operatorname{acos}{\left(- \frac{1}{8} \right)} + 2 \pi$$

x2 = acos(-1/8)

$$x_{2} = \operatorname{acos}{\left(- \frac{1}{8} \right)}$$

Сумма и произведение корней

сумма

-acos(-1/8) + 2*pi + acos(-1/8)

$$\operatorname{acos}{\left(- \frac{1}{8} \right)} + \left(- \operatorname{acos}{\left(- \frac{1}{8} \right)} + 2 \pi\right)$$

=

2*pi

$$2 \pi$$

произведение

(-acos(-1/8) + 2*pi)*acos(-1/8)

$$\left(- \operatorname{acos}{\left(- \frac{1}{8} \right)} + 2 \pi\right) \operatorname{acos}{\left(- \frac{1}{8} \right)}$$

=

(-acos(-1/8) + 2*pi)*acos(-1/8)

$$\left(- \operatorname{acos}{\left(- \frac{1}{8} \right)} + 2 \pi\right) \operatorname{acos}{\left(- \frac{1}{8} \right)}$$

Численный ответ

x1 = -54.8525436066533

x2 = -1.69612415796296

x3 = -89.6607184584772

x4 = 86.2684701425513

x5 = -61.1357289138329

x6 = 58.2447919225792

x7 = 73.7020995281921

x8 = 33.1120506938609

x9 = 14.2624947723221

x10 = 61.1357289138329

x11 = -10.8702464563962

x12 = -20.5456800795017

x13 = -95.9439037656568

x14 = -77.094347844118

x15 = 54.8525436066533

x16 = 64.5279772297588

x17 = -86.2684701425513

x18 = 39.3952360010405

x19 = 4.58706114921662

x20 = 48.5693582994737

x21 = -48.5693582994737

x22 = 67.4189142210125

x23 = -64.5279772297588

x24 = -23.4366170707554

x25 = 26.8288653866813

x26 = 142.817137907168

x27 = -14.2624947723221

x28 = 1.69612415796296

x29 = 42.2861729922941

x30 = -17.1534317635758

x31 = -165.058942144632

x32 = -33.1120506938609

x33 = 89.6607184584772

x34 = -98.8348407569104

x35 = -70.8111625369384

x36 = 95.9439037656568

x37 = -79.9852848353717

x38 = 70.8111625369384

x39 = 98.8348407569104

x40 = -26.8288653866813

x41 = 29.719802377935

x42 = -67.4189142210125

x43 = -45.6784213082201

x44 = -42.2861729922941

x45 = -36.0029876851146

x46 = 45.6784213082201

x47 = -4.58706114921662

x48 = 92.5516554497308

x49 = 79.9852848353717

x50 = 17.1534317635758

x51 = -29.719802377935

x52 = -7.97930946514255

x53 = 7.97930946514255

x54 = 77.094347844118

x55 = -92.5516554497308

x56 = -83.3775331512976

x57 = 83.3775331512976

x58 = 36.0029876851146

x59 = -39.3952360010405

x60 = -51.9616066153997

x61 = 23.4366170707554

x62 = -73.7020995281921

x63 = 10.8702464563962

x64 = 51.9616066153997

x65 = -58.2447919225792

x66 = 20.5456800795017

График