cos(x)=1/7 (уравнение)

Найду корень уравнения: cos(x)=1/7

Вы ввели

cos(x) = 1/7

$$\cos{\left(x \right)} = \frac{1}{7}$$

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = \frac{1}{7}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{7} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{7} \right)}$$
Или
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{7} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{7} \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = -acos(1/7) + 2*pi

$$x_{1} = - \operatorname{acos}{\left(\frac{1}{7} \right)} + 2 \pi$$

x2 = acos(1/7)

$$x_{2} = \operatorname{acos}{\left(\frac{1}{7} \right)}$$

Сумма и произведение корней

сумма

0 + -acos(1/7) + 2*pi + acos(1/7)

$$\operatorname{acos}{\left(\frac{1}{7} \right)} + \left(0 + \left(- \operatorname{acos}{\left(\frac{1}{7} \right)} + 2 \pi\right)\right)$$

=

2*pi

$$2 \pi$$

произведение

1*(-acos(1/7) + 2*pi)*acos(1/7)

$$1 \left(- \operatorname{acos}{\left(\frac{1}{7} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{1}{7} \right)}$$

=

(-acos(1/7) + 2*pi)*acos(1/7)

$$\left(- \operatorname{acos}{\left(\frac{1}{7} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{1}{7} \right)}$$

Численный ответ

x1 = 20.2770046794283

x2 = -95.6752283655833

x3 = 51.6929312153262

x4 = -13252.6652615996

x5 = -55.1212190067267

x6 = 99.1035161569839

x7 = 73.9707749282655

x8 = -48.8380336995472

x9 = -70.542487136865

x10 = 39.1265606009671

x11 = -13.9938193722487

x12 = -29.9884777780084

x13 = 86.5371455426247

x14 = -45.4097459081466

x15 = -61.4044043139063

x16 = 80.2539602354451

x17 = -32.8433752937875

x18 = -86.5371455426247

x19 = 57.9761165225058

x20 = 61.4044043139063

x21 = 13.9938193722487

x22 = -57.9761165225058

x23 = 32.8433752937875

x24 = -1.42744875788953

x25 = -36.271663085188

x26 = 55.1212190067267

x27 = 120.807969594302

x28 = 4.85573654929006

x29 = -17.4221071636492

x30 = 89.3920430584037

x31 = -64.2593018296854

x32 = -12017630.0530054

x33 = -67.6875896210859

x34 = 70.542487136865

x35 = 67.6875896210859

x36 = 17.4221071636492

x37 = -20.2770046794283

x38 = -83.1088577512241

x39 = 76.8256724440446

x40 = -4.85573654929006

x41 = 36.271663085188

x42 = -39.1265606009671

x43 = 26.5601899866079

x44 = 7.71063406506912

x45 = -7.71063406506912

x46 = -42.5548483923676

x47 = 23.7052924708288

x48 = 11.1389218564696

x49 = -99.1035161569839

x50 = 83.1088577512241

x51 = 42.5548483923676

x52 = -80.2539602354451

x53 = -73.9707749282655

x54 = -89.3920430584037

x55 = 45.4097459081466

x56 = 48.8380336995472

x57 = 29.9884777780084

x58 = -76.8256724440446

x59 = 64.2593018296854

x60 = -23.7052924708288

x61 = 1.42744875788953

x62 = -26.5601899866079

x63 = -11.1389218564696

x64 = 92.8203308498043

x65 = -51.6929312153262

x66 = -92.8203308498043

x67 = 95.6752283655833

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