2*sinx=1 (уравнение)

Найду корень уравнения: 2*sinx=1

Вы ввели

2*sin(x) = 1

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

Подробное решение

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

Разделим обе части ур-ния на 2

Ур-ние превратится в
$$\sin{\left(x \right)} = \frac{1}{2}$$
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 = -30.8923277602996

x2 = 2.61799387799149

x3 = -87.4409955249159

x4 = -79.0634151153431

x5 = 57.0722665402146

x6 = 40.317105721069

x7 = 82.2050077689329

x8 = 78.0162175641465

x9 = -9.94837673636768

x10 = 25.6563400043166

x11 = -24.60914245312

x12 = 17438.4572213013

x13 = 101.054563690472

x14 = 84.2994028713261

x15 = 31.9395253114962

x16 = 88.4881930761125

x17 = -97.9129710368819

x18 = -41.3643032722656

x19 = 71.733032256967

x20 = -47.6474885794452

x21 = -62.3082542961976

x22 = 138.753675533549

x23 = 38.2227106186758

x24 = -28.7979326579064

x25 = 6.80678408277789

x26 = 59.1666616426078

x27 = 94.7713783832921

x28 = -85.3466004225227

x29 = -93.7241808320955

x30 = 19.3731546971371

x31 = -5.75958653158129

x32 = -74.8746249105567

x33 = -2650.98060085419

x34 = 0.523598775598299

x35 = -49.7418836818384

x36 = -81.1578102177363

x37 = -16.2315620435473

x38 = 15.1843644923507

x39 = 90.5825881785057

x40 = 134.564885328763

x41 = 44.5058959258554

x42 = -3.66519142918809

x43 = -43.4586983746588

x44 = -66.497044500984

x45 = 46.6002910282486

x46 = -35.081117965086

x47 = 27.7507351067098

x48 = -53.9306738866248

x49 = -22.5147473507269

x50 = 8.90117918517108

x51 = 65.4498469497874

x52 = -627.79493194236

x53 = 69.6386371545737

x54 = 21.4675497995303

x55 = 96.8657734856853

x56 = -37.1755130674792

x57 = -56.025068989018

x58 = 75.9218224617533

x59 = -72.7802298081635

x60 = -18.3259571459405

x61 = 50.789081233035

x62 = -91.6297857297023

x63 = -60.2138591938044

x64 = 63.3554518473942

x65 = 34.0339204138894

x66 = -100.007366139275

x67 = 13.0899693899575

x68 = -12.0427718387609

x69 = 52.8834763354282

x70 = -68.5914396033772

x71 = -4454.25478401473

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