sin(2x)=-1/2 (уравнение)

Найду корень уравнения: sin(2x)=-1/2

Вы ввели

sin(2*x) = -1/2

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

Подробное решение

Дано уравнение
$$\sin{\left(2 x \right)} = - \frac{1}{2}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$2 x = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{2} \right)}$$
$$2 x = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{2} \right)} + \pi$$
Или
$$2 x = 2 \pi n - \frac{\pi}{6}$$
$$2 x = 2 \pi n + \frac{7 \pi}{6}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$2$$
получим ответ:
$$x_{1} = \pi n - \frac{\pi}{12}$$
$$x_{2} = \pi n + \frac{7 \pi}{12}$$

Быстрый ответ

     -pi 
x1 = ----
      12 

$$x_{1} = - \frac{\pi}{12}$$

     7*pi
x2 = ----
      12 

$$x_{2} = \frac{7 \pi}{12}$$

Численный ответ

x1 = 8.11578102177363

x2 = 127.496301858186

x3 = -13.8753675533549

x4 = 84.5612022591253

x5 = 36.3901149040818

x6 = 15.4461638801498

x7 = -20.1585528605345

x8 = 81.4196096055355

x9 = -1.30899693899575

x10 = 18.5877565337396

x11 = 1.83259571459405

x12 = 100.269165527074

x13 = 37.4373124552784

x14 = 43.720497762458

x15 = -35.8665161284835

x16 = -91.3679863419031

x17 = -97.6511716490827

x18 = -23.3001455141243

x19 = -6.54498469497874

x20 = 30.1069295969022

x21 = -88.2263936883134

x22 = -95.5567765466895

x23 = -42.1497014356631

x24 = -79.8488132787406

x25 = 65.7116463375865

x26 = 87.7027949127151

x27 = 78.2780169519457

x28 = -9.68657734856853

x29 = -53.6688744988256

x30 = 56.2868683768171

x31 = -73.565627971561

x32 = 90.8443875663049

x33 = 86.6555973615185

x34 = 59.4284610304069

x35 = 74.0892267471593

x36 = -50.5272818452358

x37 = -31.6777259236971

x38 = -64.1408500107916

x39 = 93.9859802198946

x40 = -81.9432083811338

x41 = 28.012534494509

x42 = -28.5361332701073

x43 = 14.3989663289532

x44 = -15.9697626557481

x45 = -45.2912940892529

x46 = -17.0169602069447

x47 = -86.1319985859202

x48 = 40.5789051088682

x49 = -59.9520598060052

x50 = 21.7293491873294

x51 = 12.30457122656

x52 = -0.261799387799149

x53 = 89.7971900151083

x54 = 34.2957198016886

x55 = 50.0036830696375

x56 = 71.9948316447661

x57 = -57.857664703612

x58 = 42.6733002112614

x59 = -75.6600230739542

x60 = -1926.05809603834

x61 = 62.5700536839967

x62 = 45.8148928648512

x63 = 96.0803753222878

x64 = -22.2529479629277

x65 = -37.9609112308767

x66 = -66.2352451131848

x67 = 52.0980781720307

x68 = -51.5744793964324

x69 = 23.8237442897226

x70 = 58.3812634792103

x71 = -44.2440965380563

x72 = -7.59218224617533

x73 = 67.8060414399797

x74 = -29.5833308213039

x75 = 80.3724120543389

x76 = 6.02138591938044

x77 = -67.2824426643814

x78 = -72.5184304203644

x79 = 64.6644487863899

x80 = -94.5095789954929

x81 = 20.6821516361328

x82 = -89.27359123951

График