sin(x)-1/2=0 (уравнение)

Найду корень уравнения: sin(x)-1/2=0

Вы ввели

sin(x) - 1/2 = 0

$$\sin{\left(x \right)} - \frac{1}{2} = 0$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} - \frac{1}{2} = 0$$
- это простейшее тригонометрическое ур-ние

Перенесём -1/2 в правую часть ур-ния

с изменением знака при -1/2

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

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

Численный ответ

x1 = -2650.98060085419

x2 = 71.733032256967

x3 = 94.7713783832921

x4 = 25.6563400043166

x5 = 138.753675533549

x6 = -72.7802298081635

x7 = 57.0722665402146

x8 = 50.789081233035

x9 = -97.9129710368819

x10 = -5.75958653158129

x11 = 17438.4572213013

x12 = -37.1755130674792

x13 = 46.6002910282486

x14 = -79.0634151153431

x15 = -35.081117965086

x16 = 40.317105721069

x17 = -93.7241808320955

x18 = 19.3731546971371

x19 = 15.1843644923507

x20 = -12.0427718387609

x21 = -24.60914245312

x22 = -74.8746249105567

x23 = -56.025068989018

x24 = 84.2994028713261

x25 = -91.6297857297023

x26 = -9.94837673636768

x27 = 38.2227106186758

x28 = 88.4881930761125

x29 = -4454.25478401473

x30 = 63.3554518473942

x31 = -66.497044500984

x32 = -85.3466004225227

x33 = -49.7418836818384

x34 = 13.0899693899575

x35 = 69.6386371545737

x36 = 134.564885328763

x37 = -47.6474885794452

x38 = -81.1578102177363

x39 = -41.3643032722656

x40 = -627.79493194236

x41 = 75.9218224617533

x42 = -53.9306738866248

x43 = 34.0339204138894

x44 = 96.8657734856853

x45 = -60.2138591938044

x46 = -22.5147473507269

x47 = 21.4675497995303

x48 = -68.5914396033772

x49 = 2.61799387799149

x50 = -43.4586983746588

x51 = 44.5058959258554

x52 = 27.7507351067098

x53 = -100.007366139275

x54 = 6.80678408277789

x55 = 31.9395253114962

x56 = 0.523598775598299

x57 = 78.0162175641465

x58 = -18.3259571459405

x59 = -3.66519142918809

x60 = 82.2050077689329

x61 = 101.054563690472

x62 = 90.5825881785057

x63 = -28.7979326579064

x64 = -30.8923277602996

x65 = 8.90117918517108

x66 = 52.8834763354282

x67 = -62.3082542961976

x68 = 65.4498469497874

x69 = -16.2315620435473

x70 = -87.4409955249159

x71 = 59.1666616426078

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