cos(x)=0.1 (уравнение)

Найду корень уравнения: cos(x)=0.1

Вы ввели

cos(x) = 1/10

$$\cos{\left(x \right)} = \frac{1}{10}$$

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = \frac{1}{10}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{10} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{10} \right)}$$
Или
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{10} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{10} \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = -acos(1/10) + 2*pi

$$x_{1} = - \operatorname{acos}{\left(\frac{1}{10} \right)} + 2 \pi$$

x2 = acos(1/10)

$$x_{2} = \operatorname{acos}{\left(\frac{1}{10} \right)}$$

Сумма и произведение корней

сумма

0 + -acos(1/10) + 2*pi + acos(1/10)

$$\operatorname{acos}{\left(\frac{1}{10} \right)} + \left(0 + \left(- \operatorname{acos}{\left(\frac{1}{10} \right)} + 2 \pi\right)\right)$$

=

2*pi

$$2 \pi$$

произведение

1*(-acos(1/10) + 2*pi)*acos(1/10)

$$1 \left(- \operatorname{acos}{\left(\frac{1}{10} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{1}{10} \right)}$$

=

(-acos(1/10) + 2*pi)*acos(1/10)

$$\left(- \operatorname{acos}{\left(\frac{1}{10} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{1}{10} \right)}$$

Численный ответ

x1 = -39.1697407487109

x2 = -67.6444094733421

x3 = 32.8865554415313

x4 = -76.8688525917884

x5 = 10588.6378715032

x6 = -1.47062890563334

x7 = 17.3789270159054

x8 = -58.0192966702496

x9 = -155.609003773856

x10 = 26.6033701343517

x11 = 76.8688525917884

x12 = 64.3024819774292

x13 = -99.06033600924

x14 = 14.0369995199925

x15 = -83.152037898968

x16 = -14.0369995199925

x17 = -26.6033701343517

x18 = -17.3789270159054

x19 = 80.2107800877013

x20 = -102.001593820507

x21 = -95.7184085133271

x22 = 67.6444094733421

x23 = -20.3201848271721

x24 = 1.47062890563334

x25 = 55.0780388589829

x26 = -23.662112323085

x27 = 95.7184085133271

x28 = 23.662112323085

x29 = -61.3612241661625

x30 = -36.2284829374442

x31 = -51.73611136307

x32 = -80.2107800877013

x33 = 51.73611136307

x34 = -86.4939653948809

x35 = -4.81255640154625

x36 = 36.2284829374442

x37 = -42.5116682446238

x38 = -92.7771507020605

x39 = 73.9275947805217

x40 = 89.4352232061475

x41 = -89.4352232061475

x42 = 99.06033600924

x43 = 83.152037898968

x44 = 61.3612241661625

x45 = -70.5856672846088

x46 = -55.0780388589829

x47 = -45.4529260558904

x48 = -48.7948535518034

x49 = -64.3024819774292

x50 = -32.8865554415313

x51 = 29.9452976302646

x52 = 11.0957417087258

x53 = 7.75381421281292

x54 = -73.9275947805217

x55 = 70.5856672846088

x56 = 58.0192966702496

x57 = -7.75381421281292

x58 = 102.001593820507

x59 = -11.0957417087258

x60 = 86.4939653948809

x61 = 4.81255640154625

x62 = -29.9452976302646

x63 = 39.1697407487109

x64 = 48.7948535518034

x65 = 42.5116682446238

x66 = 45.4529260558904

x67 = 92.7771507020605

x68 = 20.3201848271721

x69 = -874.833386603596

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