cos 2x =-1/2 (уравнение)

Найду корень уравнения: cos 2x =-1/2

Вы ввели

cos(2*x) = -1/2

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

Подробное решение

Дано уравнение
$$\cos{\left(2 x \right)} = - \frac{1}{2}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$2 x = \pi n + \operatorname{acos}{\left(- \frac{1}{2} \right)}$$
$$2 x = \pi n - \pi + \operatorname{acos}{\left(- \frac{1}{2} \right)}$$
Или
$$2 x = \pi n + \frac{2 \pi}{3}$$
$$2 x = \pi n - \frac{\pi}{3}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$2$$
получим ответ:
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{3}$$
$$x_{2} = \frac{\pi n}{2} - \frac{\pi}{6}$$

Быстрый ответ

     pi
x1 = --
     3 

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

     2*pi
x2 = ----
      3  

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

Численный ответ

x1 = 11.5191730631626

x2 = 77.4926187885482

x3 = 10.471975511966

x4 = -61.7846555205993

x5 = 17.8023583703422

x6 = -32.4631240870945

x7 = 79.5870138909414

x8 = -76.4454212373516

x9 = 48.1710873550435

x10 = -13.6135681655558

x11 = 98.4365698124802

x12 = 38.7463093942741

x13 = -55.5014702134197

x14 = -46.0766922526503

x15 = 52.3598775598299

x16 = 32.4631240870945

x17 = -4.18879020478639

x18 = -33.5103216382911

x19 = -83.7758040957278

x20 = -79.5870138909414

x21 = -63.8790506229925

x22 = 76.4454212373516

x23 = 61.7846555205993

x24 = 54.4542726622231

x25 = 19.8967534727354

x26 = 33.5103216382911

x27 = -70.162235930172

x28 = -49.2182849062401

x29 = -96.342174710087

x30 = 20.943951023932

x31 = -378.038315981972

x32 = -98.4365698124802

x33 = -35.6047167406843

x34 = -24.0855436775217

x35 = 4.18879020478639

x36 = -26.1799387799149

x37 = -48.1710873550435

x38 = -71.2094334813686

x39 = -60.7374579694027

x40 = 41.8879020478639

x41 = -99.4837673636768

x42 = 85.870199198121

x43 = 55.5014702134197

x44 = 70.162235930172

x45 = 82.7286065445312

x46 = -93.2005820564972

x47 = -54.4542726622231

x48 = -68.0678408277789

x49 = -294.262511886244

x50 = 1515.29485658148

x51 = -92.1533845053006

x52 = 26.1799387799149

x53 = 99.4837673636768

x54 = 2.0943951023932

x55 = -77.4926187885482

x56 = -90.0589894029074

x57 = -39.7935069454707

x58 = 92.1533845053006

x59 = -11.5191730631626

x60 = 83.7758040957278

x61 = -5.23598775598299

x62 = -27.2271363311115

x63 = 96.342174710087

x64 = 30.3687289847013

x65 = 8.37758040957278

x66 = 16.7551608191456

x67 = 39.7935069454707

x68 = -17.8023583703422

x69 = -10.471975511966

x70 = 68.0678408277789

x71 = 90.0589894029074

x72 = 60.7374579694027

x73 = -30.3687289847013

x74 = -14.6607657167524

x75 = -57.5958653158129

x76 = 24.0855436775217

x77 = 74.3510261349584

x78 = -41.8879020478639

x79 = 63.8790506229925

x80 = 46.0766922526503

x81 = -85.870199198121

x82 = -19.8967534727354

x83 = -2.0943951023932

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