sin2x=-1/2 (уравнение)

Найду корень уравнения: sin2x=-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 

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

Сумма и произведение корней

сумма

    pi   7*pi
0 - -- + ----
    12    12 

$$\left(- \frac{\pi}{12} + 0\right) + \frac{7 \pi}{12}$$

=

pi
--
2 

$$\frac{\pi}{2}$$

произведение

  -pi  7*pi
1*----*----
   12   12 

$$\frac{7 \pi}{12} \cdot 1 \left(- \frac{\pi}{12}\right)$$

=

     2
-7*pi 
------
 144  

$$- \frac{7 \pi^{2}}{144}$$

Численный ответ

x1 = 42.6733002112614

x2 = 65.7116463375865

x3 = -45.2912940892529

x4 = 1.83259571459405

x5 = -23.3001455141243

x6 = 28.012534494509

x7 = -72.5184304203644

x8 = -95.5567765466895

x9 = 58.3812634792103

x10 = 8.11578102177363

x11 = 81.4196096055355

x12 = 86.6555973615185

x13 = -66.2352451131848

x14 = -15.9697626557481

x15 = 43.720497762458

x16 = -94.5095789954929

x17 = 45.8148928648512

x18 = 52.0980781720307

x19 = -1.30899693899575

x20 = -59.9520598060052

x21 = 6.02138591938044

x22 = 80.3724120543389

x23 = -44.2440965380563

x24 = 71.9948316447661

x25 = -81.9432083811338

x26 = 89.7971900151083

x27 = -28.5361332701073

x28 = -51.5744793964324

x29 = -1926.05809603834

x30 = 90.8443875663049

x31 = 40.5789051088682

x32 = 37.4373124552784

x33 = 62.5700536839967

x34 = 12.30457122656

x35 = -97.6511716490827

x36 = -67.2824426643814

x37 = -31.6777259236971

x38 = 23.8237442897226

x39 = -6.54498469497874

x40 = -91.3679863419031

x41 = 93.9859802198946

x42 = 100.269165527074

x43 = -17.0169602069447

x44 = 67.8060414399797

x45 = 15.4461638801498

x46 = -20.1585528605345

x47 = -50.5272818452358

x48 = 74.0892267471593

x49 = -53.6688744988256

x50 = 78.2780169519457

x51 = -86.1319985859202

x52 = 56.2868683768171

x53 = -73.565627971561

x54 = -22.2529479629277

x55 = 127.496301858186

x56 = -0.261799387799149

x57 = 34.2957198016886

x58 = -42.1497014356631

x59 = 50.0036830696375

x60 = -29.5833308213039

x61 = 96.0803753222878

x62 = 14.3989663289532

x63 = 59.4284610304069

x64 = 30.1069295969022

x65 = 64.6644487863899

x66 = -57.857664703612

x67 = -64.1408500107916

x68 = 84.5612022591253

x69 = -9.68657734856853

x70 = -37.9609112308767

x71 = -75.6600230739542

x72 = -88.2263936883134

x73 = -89.27359123951

x74 = 20.6821516361328

x75 = 18.5877565337396

x76 = 21.7293491873294

x77 = 87.7027949127151

x78 = -7.59218224617533

x79 = -35.8665161284835

x80 = -79.8488132787406

x81 = -13.8753675533549

x82 = 36.3901149040818

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