2 cos x = -1 (уравнение)

Найду корень уравнения: 2 cos x = -1

Вы ввели

2*cos(x) = -1

$$2 \cos{\left(x \right)} = -1$$

Подробное решение

Дано уравнение
$$2 \cos{\left(x \right)} = -1$$
- это простейшее тригонометрическое ур-ние

Разделим обе части ур-ния на 2

Ур-ние превратится в
$$\cos{\left(x \right)} = - \frac{1}{2}$$
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(- \frac{1}{2} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{1}{2} \right)}$$
Или
$$x = \pi n + \frac{2 \pi}{3}$$
$$x = \pi n - \frac{\pi}{3}$$
, где n - любое целое число

Быстрый ответ

     2*pi
x1 = ----
      3  

$$x_{1} = \frac{2 \pi}{3}$$

     4*pi
x2 = ----
      3  

$$x_{2} = \frac{4 \pi}{3}$$

Численный ответ

x1 = 85.870199198121

x2 = -20.943951023932

x3 = -14.6607657167524

x4 = -90.0589894029074

x5 = -54.4542726622231

x6 = 58.6430628670095

x7 = -35.6047167406843

x8 = -2.0943951023932

x9 = 92.1533845053006

x10 = -27.2271363311115

x11 = 67.0206432765823

x12 = -58.6430628670095

x13 = -41.8879020478639

x14 = -10.471975511966

x15 = 39.7935069454707

x16 = 2.0943951023932

x17 = 41.8879020478639

x18 = -64.9262481741891

x19 = -60.7374579694027

x20 = 83.7758040957278

x21 = -29.3215314335047

x22 = -73.3038285837618

x23 = 48.1710873550435

x24 = 54.4542726622231

x25 = -33.5103216382911

x26 = -39.7935069454707

x27 = 64.9262481741891

x28 = 77.4926187885482

x29 = 46.0766922526503

x30 = -52.3598775598299

x31 = -79.5870138909414

x32 = -23.0383461263252

x33 = -77.4926187885482

x34 = 73.3038285837618

x35 = 90.0589894029074

x36 = -71.2094334813686

x37 = 98.4365698124802

x38 = 117.286125734019

x39 = -85.870199198121

x40 = 16.7551608191456

x41 = 35.6047167406843

x42 = -1623.15620435473

x43 = -67.0206432765823

x44 = 71.2094334813686

x45 = 8.37758040957278

x46 = 416.784625376246

x47 = 27.2271363311115

x48 = 10.471975511966

x49 = 630.412925820352

x50 = -48.1710873550435

x51 = -83.7758040957278

x52 = 33.5103216382911

x53 = -96.342174710087

x54 = 23.0383461263252

x55 = -8.37758040957278

x56 = -16.7551608191456

x57 = 29.3215314335047

x58 = 60.7374579694027

x59 = 4.18879020478639

x60 = -98.4365698124802

x61 = -92.1533845053006

x62 = 52.3598775598299

x63 = 79.5870138909414

x64 = 20.943951023932

x65 = -46.0766922526503

x66 = -4.18879020478639

x67 = 14.6607657167524

x68 = 96.342174710087

График