cosx=-1/2 (уравнение)

Найду корень уравнения: cosx=-1/2

Вы ввели

cos(x) = -1/2

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

Подробное решение

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

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

Сумма и произведение корней

сумма

    2*pi   4*pi
0 + ---- + ----
     3      3  

$$\left(0 + \frac{2 \pi}{3}\right) + \frac{4 \pi}{3}$$

=

2*pi

$$2 \pi$$

произведение

  2*pi 4*pi
1*----*----
   3    3  

$$\frac{4 \pi}{3} \cdot 1 \cdot \frac{2 \pi}{3}$$

=

    2
8*pi 
-----
  9  

$$\frac{8 \pi^{2}}{9}$$

Численный ответ

x1 = 29.3215314335047

x2 = 27.2271363311115

x3 = 90.0589894029074

x4 = -23.0383461263252

x5 = -58.6430628670095

x6 = -52.3598775598299

x7 = -35.6047167406843

x8 = 10.471975511966

x9 = 2.0943951023932

x10 = 73.3038285837618

x11 = 8.37758040957278

x12 = 96.342174710087

x13 = 77.4926187885482

x14 = 35.6047167406843

x15 = 58.6430628670095

x16 = -67.0206432765823

x17 = -79.5870138909414

x18 = -64.9262481741891

x19 = 117.286125734019

x20 = 67.0206432765823

x21 = 33.5103216382911

x22 = 83.7758040957278

x23 = 416.784625376246

x24 = -20.943951023932

x25 = 23.0383461263252

x26 = 54.4542726622231

x27 = -8.37758040957278

x28 = 20.943951023932

x29 = 4.18879020478639

x30 = -48.1710873550435

x31 = 85.870199198121

x32 = -14.6607657167524

x33 = -16.7551608191456

x34 = -96.342174710087

x35 = 60.7374579694027

x36 = -41.8879020478639

x37 = 41.8879020478639

x38 = -33.5103216382911

x39 = 630.412925820352

x40 = -71.2094334813686

x41 = 98.4365698124802

x42 = 71.2094334813686

x43 = -92.1533845053006

x44 = -54.4542726622231

x45 = -85.870199198121

x46 = -4.18879020478639

x47 = 92.1533845053006

x48 = -98.4365698124802

x49 = 48.1710873550435

x50 = -46.0766922526503

x51 = -39.7935069454707

x52 = -90.0589894029074

x53 = -29.3215314335047

x54 = 52.3598775598299

x55 = -27.2271363311115

x56 = -1623.15620435473

x57 = 39.7935069454707

x58 = -10.471975511966

x59 = 46.0766922526503

x60 = -77.4926187885482

x61 = 64.9262481741891

x62 = -83.7758040957278

x63 = 14.6607657167524

x64 = 79.5870138909414

x65 = -2.0943951023932

x66 = -60.7374579694027

x67 = 16.7551608191456

x68 = -73.3038285837618

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