sin(x)=0.5 (уравнение)

Найду корень уравнения: sin(x)=0.5

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 = -12.0427718387609

x2 = 34.0339204138894

x3 = 2.61799387799149

x4 = -41.3643032722656

x5 = 6.80678408277789

x6 = 8.90117918517108

x7 = -2650.98060085419

x8 = 40.317105721069

x9 = -16.2315620435473

x10 = -85.3466004225227

x11 = 0.523598775598299

x12 = 65.4498469497874

x13 = -93.7241808320955

x14 = 71.733032256967

x15 = 31.9395253114962

x16 = 44.5058959258554

x17 = -68.5914396033772

x18 = -43.4586983746588

x19 = -24.60914245312

x20 = -3.66519142918809

x21 = -60.2138591938044

x22 = 50.789081233035

x23 = -100.007366139275

x24 = -87.4409955249159

x25 = 38.2227106186758

x26 = 138.753675533549

x27 = 96.8657734856853

x28 = -5.75958653158129

x29 = 57.0722665402146

x30 = 88.4881930761125

x31 = 27.7507351067098

x32 = 19.3731546971371

x33 = -18.3259571459405

x34 = 90.5825881785057

x35 = 84.2994028713261

x36 = -37.1755130674792

x37 = -22.5147473507269

x38 = -81.1578102177363

x39 = -74.8746249105567

x40 = 94.7713783832921

x41 = 15.1843644923507

x42 = 134.564885328763

x43 = -91.6297857297023

x44 = -79.0634151153431

x45 = -62.3082542961976

x46 = -4454.25478401473

x47 = -9.94837673636768

x48 = 17438.4572213013

x49 = 25.6563400043166

x50 = 59.1666616426078

x51 = -66.497044500984

x52 = -53.9306738866248

x53 = 21.4675497995303

x54 = -28.7979326579064

x55 = 82.2050077689329

x56 = -56.025068989018

x57 = 69.6386371545737

x58 = 63.3554518473942

x59 = 52.8834763354282

x60 = 13.0899693899575

x61 = -30.8923277602996

x62 = -72.7802298081635

x63 = 78.0162175641465

x64 = -49.7418836818384

x65 = 101.054563690472

x66 = 75.9218224617533

x67 = -97.9129710368819

x68 = -47.6474885794452

x69 = -627.79493194236

x70 = -35.081117965086

x71 = 46.6002910282486

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