cos(x)=-1/4 (уравнение)

Найду корень уравнения: cos(x)=-1/4

Вы ввели

cos(x) = -1/4

$$\cos{\left(x \right)} = - \frac{1}{4}$$

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = - \frac{1}{4}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(- \frac{1}{4} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{1}{4} \right)}$$
Или
$$x = \pi n + \operatorname{acos}{\left(- \frac{1}{4} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{1}{4} \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = -acos(-1/4) + 2*pi

$$x_{1} = - \operatorname{acos}{\left(- \frac{1}{4} \right)} + 2 \pi$$

x2 = acos(-1/4)

$$x_{2} = \operatorname{acos}{\left(- \frac{1}{4} \right)}$$

Сумма и произведение корней

сумма

0 + -acos(-1/4) + 2*pi + acos(-1/4)

$$\operatorname{acos}{\left(- \frac{1}{4} \right)} + \left(0 + \left(- \operatorname{acos}{\left(- \frac{1}{4} \right)} + 2 \pi\right)\right)$$

=

2*pi

$$2 \pi$$

произведение

1*(-acos(-1/4) + 2*pi)*acos(-1/4)

$$1 \left(- \operatorname{acos}{\left(- \frac{1}{4} \right)} + 2 \pi\right) \operatorname{acos}{\left(- \frac{1}{4} \right)}$$

=

(-acos(-1/4) + 2*pi)*acos(-1/4)

$$\left(- \operatorname{acos}{\left(- \frac{1}{4} \right)} + 2 \pi\right) \operatorname{acos}{\left(- \frac{1}{4} \right)}$$

Численный ответ

x1 = 61.0083764898589

x2 = 14.3898471962961

x3 = 10.7428940324222

x4 = -29.592449953961

x5 = 8.10666188911656

x6 = -73.5747471042181

x7 = 26.9562178106553

x8 = -1.82347658193698

x9 = -86.1411177185772

x10 = 86.1411177185772

x11 = 39.5225884250145

x12 = -58.3721443465533

x13 = -23.3092646467814

x14 = 98.7074883329364

x15 = -64.6553296537328

x16 = -26.9562178106553

x17 = 83.5048855752716

x18 = 1.82347658193698

x19 = 58.3721443465533

x20 = -98.7074883329364

x21 = -45.8057737321941

x22 = 45.8057737321941

x23 = 79.8579324113977

x24 = -33.2394031178349

x25 = 89.7880708824512

x26 = 67.2915617970385

x27 = -17.0260793396018

x28 = -67.2915617970385

x29 = -54.7251911826793

x30 = 20.6730325034757

x31 = -83.5048855752716

x32 = 73.5747471042181

x33 = -92.4243030257568

x34 = -61.0083764898589

x35 = 29.592449953961

x36 = 33.2394031178349

x37 = -42.1588205683201

x38 = -4.45970872524261

x39 = 52.0889590393737

x40 = -79.8579324113977

x41 = -39.5225884250145

x42 = -77.221700268092

x43 = 35.8756352611405

x44 = -52.0889590393737

x45 = 92.4243030257568

x46 = -89.7880708824512

x47 = 48.4420058754997

x48 = -10.7428940324222

x49 = -35.8756352611405

x50 = 23.3092646467814

x51 = -14.3898471962961

x52 = 17.0260793396018

x53 = 96.0712561896308

x54 = 42.1588205683201

x55 = 54.7251911826793

x56 = 77.221700268092

x57 = -20.6730325034757

x58 = -48.4420058754997

x59 = 70.9385149609124

x60 = -70.9385149609124

x61 = 4.45970872524261

x62 = 64.6553296537328

x63 = -96.0712561896308

x64 = -8.10666188911656

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