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
$$x = 2 \pi n + \frac{\pi}{6}$$
$$x = 2 \pi n + \frac{5 \pi}{6}$$
, где n - любое целое число

Быстрый ответ

     pi
x1 = --
     6 

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

     5*pi
x2 = ----
      6  

$$x_{2} = \frac{5 \pi}{6}$$

Сумма и произведение корней

сумма

    pi   5*pi
0 + -- + ----
    6     6  

$$\left(0 + \frac{\pi}{6}\right) + \frac{5 \pi}{6}$$

=

pi

$$\pi$$

произведение

  pi 5*pi
1*--*----
  6   6  

$$\frac{5 \pi}{6} \cdot 1 \frac{\pi}{6}$$

=

    2
5*pi 
-----
  36 

$$\frac{5 \pi^{2}}{36}$$

Численный ответ

x1 = -62.3082542961976

x2 = 6.80678408277789

x3 = -49.7418836818384

x4 = -5.75958653158129

x5 = -37.1755130674792

x6 = -66.497044500984

x7 = -81.1578102177363

x8 = 94.7713783832921

x9 = -4454.25478401473

x10 = 134.564885328763

x11 = 52.8834763354282

x12 = -87.4409955249159

x13 = -60.2138591938044

x14 = -74.8746249105567

x15 = 82.2050077689329

x16 = 101.054563690472

x17 = 65.4498469497874

x18 = 13.0899693899575

x19 = 21.4675497995303

x20 = -47.6474885794452

x21 = 40.317105721069

x22 = 50.789081233035

x23 = -72.7802298081635

x24 = -12.0427718387609

x25 = -93.7241808320955

x26 = 34.0339204138894

x27 = 25.6563400043166

x28 = -9.94837673636768

x29 = 0.523598775598299

x30 = 15.1843644923507

x31 = -79.0634151153431

x32 = 69.6386371545737

x33 = 44.5058959258554

x34 = 75.9218224617533

x35 = -85.3466004225227

x36 = 59.1666616426078

x37 = 88.4881930761125

x38 = 57.0722665402146

x39 = 71.733032256967

x40 = -22.5147473507269

x41 = -35.081117965086

x42 = 138.753675533549

x43 = -56.025068989018

x44 = -100.007366139275

x45 = -30.8923277602996

x46 = 63.3554518473942

x47 = 2.61799387799149

x48 = 78.0162175641465

x49 = -97.9129710368819

x50 = -16.2315620435473

x51 = 46.6002910282486

x52 = 38.2227106186758

x53 = -91.6297857297023

x54 = -3.66519142918809

x55 = -627.79493194236

x56 = -28.7979326579064

x57 = -43.4586983746588

x58 = -53.9306738866248

x59 = 96.8657734856853

x60 = 84.2994028713261

x61 = 8.90117918517108

x62 = -68.5914396033772

x63 = -2650.98060085419

x64 = -41.3643032722656

x65 = 17438.4572213013

x66 = -18.3259571459405

x67 = 31.9395253114962

x68 = 19.3731546971371

x69 = 27.7507351067098

x70 = -24.60914245312

x71 = 90.5825881785057

График