cos(2x)=-1/3 (уравнение)

Найду корень уравнения: cos(2x)=-1/3

Вы ввели

cos(2*x) = -1/3

$$\cos{\left(2 x \right)} = - \frac{1}{3}$$

Подробное решение

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

Быстрый ответ

          acos(-1/3)
x1 = pi - ----------
              2     

$$x_{1} = \pi - \frac{\operatorname{acos}{\left(- \frac{1}{3} \right)}}{2}$$

     acos(-1/3)
x2 = ----------
         2     

$$x_{2} = \frac{\operatorname{acos}{\left(- \frac{1}{3} \right)}}{2}$$

Численный ответ

x1 = 41.7960211147918

x2 = 4.0969092717143

x3 = 2653.69047566525

x4 = 76.3535403042795

x5 = -63.7871696899204

x6 = -26.0880578468429

x7 = 33.6022025713632

x8 = 52.451758492902

x9 = 11.6110539962347

x10 = -11.6110539962347

x11 = -61.8765364536714

x12 = -60.6455770363306

x13 = 10.3800945788939

x14 = -80.7260923752101

x15 = 79.4951329578693

x16 = -76.3535403042795

x17 = -54.362391729151

x18 = -79.4951329578693

x19 = -2.18627603546528

x20 = 77.5844997216203

x21 = 44.9376137683816

x22 = -77.5844997216203

x23 = 85.7783182650489

x24 = -71.3013144144407

x25 = -117.194244800947

x26 = 70.0703549971

x27 = -83.8676850287999

x28 = 98.3446888794081

x29 = -10.3800945788939

x30 = 2.18627603546528

x31 = 61.8765364536714

x32 = -85.7783182650489

x33 = 174.973871982904

x34 = 26.0880578468429

x35 = 60.6455770363306

x36 = 32.3712431540224

x37 = 48.0792064219714

x38 = -90.1508703359795

x39 = -48.0792064219714

x40 = -33.6022025713632

x41 = -4.0969092717143

x42 = 8.46946134264487

x43 = 74.4429070680305

x44 = 63.7871696899204

x45 = -98.3446888794081

x46 = -19.8048725396633

x47 = 82.6367256114591

x48 = 99.5756482967489

x49 = 87.0092776823897

x50 = 39.8853878785428

x51 = -27.3190172641836

x52 = 19.8048725396633

x53 = 0.955316618124509

x54 = -55.5933511464918

x55 = -92.0615035722285

x56 = 38.654428461202

x57 = -5.32786868905508

x58 = -32.3712431540224

x59 = 17.8942393034142

x60 = -46.1685731857224

x61 = -99.5756482967489

x62 = 198.875653794281

x63 = -70.0703549971

x64 = -49.3101658393122

x65 = -35.5128358076122

x66 = 16.6632798860735

x67 = 92.0615035722285

x68 = 90.1508703359795

x69 = 54.362391729151

x70 = 68.1597217608509

x71 = 30.4606099177734

x72 = -17.8942393034142

x73 = 83.8676850287999

x74 = -93.2924629895693

x75 = 46.1685731857224

x76 = 55.5933511464918

x77 = -24.1774246105938

x78 = -57.5039843827408

x79 = -13.5216872324837

x80 = -41.7960211147918

x81 = 24.1774246105938

x82 = 96.4340556431591

x83 = -68.1597217608509

x84 = -39.8853878785428

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