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

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)

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

Быстрый ответ

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

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

x2 = acos(-1/10)

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

Численный ответ

x1 = 36.0281480951211

x2 = 89.6355580484707

x3 = 42.3113334023006

x4 = 51.9364462053931

x5 = -23.4617774807619

x6 = 1679.28144076491

x7 = -67.444074631019

x8 = 26.8037049766748

x9 = -20.5205196694952

x10 = -95.9187433556502

x11 = 45.6532608982136

x12 = -58.2196315125727

x13 = 95.9187433556502

x14 = 98.8600011669169

x15 = -54.8777040166598

x16 = 4.61222155922313

x17 = -36.0281480951211

x18 = -42.3113334023006

x19 = -17.1785921735823

x20 = 92.5768158597373

x21 = 39.370075591034

x22 = -10.8954068664027

x23 = 17.1785921735823

x24 = 70.7860021269319

x25 = -73.7272599381986

x26 = 61.1608893238394

x27 = 86.2936305525578

x28 = -26.8037049766748

x29 = -48.5945187094802

x30 = -64.5028168197523

x31 = 14.2373343623156

x32 = -86.2936305525578

x33 = 67.444074631019

x34 = 64.5028168197523

x35 = -61.1608893238394

x36 = -102.20192866283

x37 = 126714.669053639

x38 = 7.95414905513604

x39 = -51.9364462053931

x40 = 29.7449627879415

x41 = -16598.5046178205

x42 = -4.61222155922313

x43 = -70.7860021269319

x44 = -14.2373343623156

x45 = -98.8600011669169

x46 = 48.5945187094802

x47 = -7.95414905513604

x48 = -89.6355580484707

x49 = -83.3523727412911

x50 = -92.5768158597373

x51 = 54.8777040166598

x52 = 20.5205196694952

x53 = 10.8954068664027

x54 = 33.0868902838544

x55 = -1.67096374795646

x56 = 83.3523727412911

x57 = -29.7449627879415

x58 = 77.0691874341115

x59 = -77.0691874341115

x60 = -80.0104452453782

x61 = 1.67096374795646

x62 = -39.370075591034

x63 = 73.7272599381986

x64 = -45.6532608982136

x65 = 23.4617774807619

x66 = -33.0868902838544

x67 = 80.0104452453782

x68 = 58.2196315125727

x69 = 746.028087806414

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