sin(x)=-1/2 (уравнение)

Найду корень уравнения: sin(x)=-1/2

Вы ввели

sin(x) = -1/2

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

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = - \frac{1}{2}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{2} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{2} \right)} + \pi$$
Или
$$x = 2 \pi n - \frac{\pi}{6}$$
$$x = 2 \pi n + \frac{7 \pi}{6}$$
, где n - любое целое число

Быстрый ответ

     -pi 
x1 = ----
      6  

$$x_{1} = - \frac{\pi}{6}$$

     7*pi
x2 = ----
      6  

$$x_{2} = \frac{7 \pi}{6}$$

Сумма и произведение корней

сумма

    pi   7*pi
0 - -- + ----
    6     6  

$$\left(- \frac{\pi}{6} + 0\right) + \frac{7 \pi}{6}$$

=

pi

$$\pi$$

произведение

  -pi  7*pi
1*----*----
   6    6  

$$\frac{7 \pi}{6} \cdot 1 \left(- \frac{\pi}{6}\right)$$

=

     2
-7*pi 
------
  36  

$$- \frac{7 \pi^{2}}{36}$$

Численный ответ

x1 = 97.9129710368819

x2 = 37.1755130674792

x3 = -96.8657734856853

x4 = -151.320046147908

x5 = 74.8746249105567

x6 = -101.054563690472

x7 = 66400.1787274983

x8 = 28.7979326579064

x9 = -46.6002910282486

x10 = 53.9306738866248

x11 = -90.5825881785057

x12 = 81.1578102177363

x13 = -94.7713783832921

x14 = -71.733032256967

x15 = 91.6297857297023

x16 = -50.789081233035

x17 = 24.60914245312

x18 = 100.007366139275

x19 = 437.20497762458

x20 = 66.497044500984

x21 = -19.3731546971371

x22 = 60.2138591938044

x23 = 68.5914396033772

x24 = 9.94837673636768

x25 = 41.3643032722656

x26 = -65.4498469497874

x27 = 43.4586983746588

x28 = 72.7802298081635

x29 = -195.302343298165

x30 = -0.523598775598299

x31 = -52.8834763354282

x32 = -27.7507351067098

x33 = -84.2994028713261

x34 = 79.0634151153431

x35 = -75.9218224617533

x36 = 30.8923277602996

x37 = 18.3259571459405

x38 = 47.6474885794452

x39 = -15.1843644923507

x40 = 3.66519142918809

x41 = -21.4675497995303

x42 = -63.3554518473942

x43 = -40.317105721069

x44 = -78.0162175641465

x45 = -34.0339204138894

x46 = -38.2227106186758

x47 = 93.7241808320955

x48 = -31.9395253114962

x49 = -25.6563400043166

x50 = -2.61799387799149

x51 = -69.6386371545737

x52 = 12.0427718387609

x53 = 87.4409955249159

x54 = -57.0722665402146

x55 = 85.3466004225227

x56 = -59.1666616426078

x57 = 35.081117965086

x58 = -44.5058959258554

x59 = -13.0899693899575

x60 = -82.2050077689329

x61 = -8.90117918517108

x62 = 49.7418836818384

x63 = 62.3082542961976

x64 = 56.025068989018

x65 = 5.75958653158129

x66 = 192.160750644576

x67 = -6.80678408277789

x68 = -88.4881930761125

x69 = 22.5147473507269

x70 = 16.2315620435473

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