sin(y)=1/2 (уравнение)

Найду корень уравнения: sin(y)=1/2

Вы ввели

sin(y) = 1/2

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

Подробное решение

Дано уравнение
$$\sin{\left(y \right)} = \frac{1}{2}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$y = 2 \pi n + \operatorname{asin}{\left(\frac{1}{2} \right)}$$
$$y = 2 \pi n - \operatorname{asin}{\left(\frac{1}{2} \right)} + \pi$$
Или
$$y = 2 \pi n + \frac{\pi}{6}$$
$$y = 2 \pi n + \frac{5 \pi}{6}$$
, где n - любое целое число

Быстрый ответ

     pi
y1 = --
     6 

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

     5*pi
y2 = ----
      6  

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

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

y1 = -12.0427718387609

y2 = 34.0339204138894

y3 = 2.61799387799149

y4 = -41.3643032722656

y5 = 6.80678408277789

y6 = 8.90117918517108

y7 = -2650.98060085419

y8 = 40.317105721069

y9 = -16.2315620435473

y10 = -85.3466004225227

y11 = 0.523598775598299

y12 = 65.4498469497874

y13 = -93.7241808320955

y14 = 71.733032256967

y15 = 31.9395253114962

y16 = 44.5058959258554

y17 = -68.5914396033772

y18 = -43.4586983746588

y19 = -24.60914245312

y20 = -3.66519142918809

y21 = -60.2138591938044

y22 = 50.789081233035

y23 = -100.007366139275

y24 = -87.4409955249159

y25 = 38.2227106186758

y26 = 138.753675533549

y27 = 96.8657734856853

y28 = -5.75958653158129

y29 = 57.0722665402146

y30 = 88.4881930761125

y31 = 27.7507351067098

y32 = 19.3731546971371

y33 = -18.3259571459405

y34 = 90.5825881785057

y35 = 84.2994028713261

y36 = -37.1755130674792

y37 = -22.5147473507269

y38 = -81.1578102177363

y39 = -74.8746249105567

y40 = 94.7713783832921

y41 = 15.1843644923507

y42 = 134.564885328763

y43 = -91.6297857297023

y44 = -79.0634151153431

y45 = -62.3082542961976

y46 = -4454.25478401473

y47 = -9.94837673636768

y48 = 17438.4572213013

y49 = 25.6563400043166

y50 = 59.1666616426078

y51 = -66.497044500984

y52 = -53.9306738866248

y53 = 21.4675497995303

y54 = -28.7979326579064

y55 = 82.2050077689329

y56 = -56.025068989018

y57 = 69.6386371545737

y58 = 63.3554518473942

y59 = 52.8834763354282

y60 = 13.0899693899575

y61 = -30.8923277602996

y62 = -72.7802298081635

y63 = 78.0162175641465

y64 = -49.7418836818384

y65 = 101.054563690472

y66 = 75.9218224617533

y67 = -97.9129710368819

y68 = -47.6474885794452

y69 = -627.79493194236

y70 = -35.081117965086

y71 = 46.6002910282486

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