cos(x)=0,2 (уравнение)

Найду корень уравнения: cos(x)=0,2

Вы ввели

cos(x) = 1/5

$$\cos{\left(x \right)} = \frac{1}{5}$$

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = \frac{1}{5}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{5} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{5} \right)}$$
Или
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{5} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{5} \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = -acos(1/5) + 2*pi

$$x_{1} = - \operatorname{acos}{\left(\frac{1}{5} \right)} + 2 \pi$$

x2 = acos(1/5)

$$x_{2} = \operatorname{acos}{\left(\frac{1}{5} \right)}$$

Сумма и произведение корней

сумма

-acos(1/5) + 2*pi + acos(1/5)

$$\operatorname{acos}{\left(\frac{1}{5} \right)} + \left(- \operatorname{acos}{\left(\frac{1}{5} \right)} + 2 \pi\right)$$

=

2*pi

$$2 \pi$$

произведение

(-acos(1/5) + 2*pi)*acos(1/5)

$$\left(- \operatorname{acos}{\left(\frac{1}{5} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{1}{5} \right)}$$

=

(-acos(1/5) + 2*pi)*acos(1/5)

$$\left(- \operatorname{acos}{\left(\frac{1}{5} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{1}{5} \right)}$$

Численный ответ

x1 = 45.3517355562617

x2 = 11.1969322083546

x3 = 13.9358090203637

x4 = 4.91374690117502

x5 = -7.65262371318415

x6 = -1.36943840600457

x7 = 36.329673437073

x8 = 70.48447678498

x9 = -80.3119705873301

x10 = 23.7633028227138

x11 = 1.36943840600457

x12 = -4.91374690117502

x13 = 76.7676620921596

x14 = -39.0685502490821

x15 = 67.7455999729709

x16 = -26.5021796347229

x17 = 74.0287852801505

x18 = 39.0685502490821

x19 = -17.4801175155342

x20 = 80.3119705873301

x21 = 48.8960440514321

x22 = -23.7633028227138

x23 = 89.3340327065188

x24 = -99.1615265088688

x25 = 51.6349208634413

x26 = 20.2189943275433

x27 = 42.6128587442525

x28 = -74.0287852801505

x29 = -92.8783412016892

x30 = -51.6349208634413

x31 = 92.8783412016892

x32 = -20.2189943275433

x33 = 108.183588628058

x34 = 99.1615265088688

x35 = 17.4801175155342

x36 = 64.2012914778004

x37 = -83.0508473993392

x38 = 30.0464881298934

x39 = 834.29420744888

x40 = -36.329673437073

x41 = -67.7455999729709

x42 = -32.7853649419025

x43 = -55.1792293586117

x44 = -64.2012914778004

x45 = -42.6128587442525

x46 = -30.0464881298934

x47 = 7.65262371318415

x48 = 86.5951558945096

x49 = 61.4624146657913

x50 = -89.3340327065188

x51 = -11.1969322083546

x52 = 83.0508473993392

x53 = -45.3517355562617

x54 = 55.1792293586117

x55 = 95.6172180136984

x56 = -95.6172180136984

x57 = 32.7853649419025

x58 = -61.4624146657913

x59 = -76.7676620921596

x60 = -48.8960440514321

x61 = -654.820710352682

x62 = -86.5951558945096

x63 = -57.9181061706208

x64 = 57.9181061706208

x65 = -70.48447678498

x66 = 26.5021796347229

x67 = -13.9358090203637

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