cos(x)=-1/5 (уравнение)

Найду корень уравнения: cos(x)=-1/5

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

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

$$\operatorname{acos}{\left(- \frac{1}{5} \right)} + \left(0 + \left(- \operatorname{acos}{\left(- \frac{1}{5} \right)} + 2 \pi\right)\right)$$

=

2*pi

$$2 \pi$$

произведение

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

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

=

(-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 = -17.0774016739535

x2 = -2458.4976093548

x3 = -23.3605869811331

x4 = -67.3428841313902

x5 = 61.0596988242106

x6 = 4.51103105959436

x7 = 79.9092547457494

x8 = 17.0774016739535

x9 = -26.9048954763036

x10 = 29.6437722883127

x11 = 86.192440052929

x12 = -77.1703779337403

x13 = 48.4933282098515

x14 = -39.4712660906627

x15 = 39.4712660906627

x16 = -73.6260694385698

x17 = 26.9048954763036

x18 = -89.7367485480994

x19 = 52.0376367050219

x20 = 33.1880807834832

x21 = 83.4535632409198

x22 = 98.7588106672882

x23 = -48.4933282098515

x24 = -4.51103105959436

x25 = -92.4756253601086

x26 = -70.8871926265607

x27 = -42.2101429026719

x28 = 10.7942163667739

x29 = 54.776513517031

x30 = -33.1880807834832

x31 = 92.4756253601086

x32 = 35.9269575954923

x33 = -45.7544513978423

x34 = 58.3208220122015

x35 = -61.0596988242106

x36 = -35.9269575954923

x37 = -96.019933855279

x38 = -64.6040073193811

x39 = -8.05533955476481

x40 = 77.1703779337403

x41 = 70.8871926265607

x42 = -52.0376367050219

x43 = 67.3428841313902

x44 = 42.2101429026719

x45 = 45.7544513978423

x46 = 2699.99752783964

x47 = 1.77215424758523

x48 = 20.621710169124

x49 = -1.77215424758523

x50 = -58.3208220122015

x51 = -20.621710169124

x52 = 89.7367485480994

x53 = 23.3605869811331

x54 = -79.9092547457494

x55 = 14.3385248619444

x56 = -83.4535632409198

x57 = -86.192440052929

x58 = -14.3385248619444

x59 = 8.05533955476481

x60 = 96.019933855279

x61 = 64.6040073193811

x62 = -54.776513517031

x63 = -29.6437722883127

x64 = 73.6260694385698

x65 = -10.7942163667739

x66 = -98.7588106672882

График