sin2x=√3/2 (уравнение)

Найду корень уравнения: sin2x=√3/2

Вы ввели

             ___
           \/ 3 
sin(2*x) = -----
             2  

$$\sin{\left(2 x \right)} = \frac{\sqrt{3}}{2}$$

Подробное решение

Дано уравнение
$$\sin{\left(2 x \right)} = \frac{\sqrt{3}}{2}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$2 x = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{3}}{2} \right)}$$
$$2 x = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{3}}{2} \right)} + \pi$$
Или
$$2 x = 2 \pi n + \frac{\pi}{3}$$
$$2 x = 2 \pi n + \frac{2 \pi}{3}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$2$$
получим ответ:
$$x_{1} = \pi n + \frac{\pi}{6}$$
$$x_{2} = \pi n + \frac{\pi}{3}$$

Быстрый ответ

     pi
x1 = --
     6 

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

     pi
x2 = --
     3 

$$x_{2} = \frac{\pi}{3}$$

Сумма и произведение корней

сумма

    pi   pi
0 + -- + --
    6    3 

$$\left(0 + \frac{\pi}{6}\right) + \frac{\pi}{3}$$

=

pi
--
2 

$$\frac{\pi}{2}$$

произведение

  pi pi
1*--*--
  6  3 

$$\frac{\pi}{3} \cdot 1 \frac{\pi}{6}$$

=

  2
pi 
---
 18

$$\frac{\pi^{2}}{18}$$

Численный ответ

x1 = 63.8790506229925

x2 = -37.1755130674792

x3 = 28.7979326579064

x4 = -87.4409955249159

x5 = -83.7758040957278

x6 = 70.162235930172

x7 = 72.7802298081635

x8 = -52.3598775598299

x9 = -12.0427718387609

x10 = -93.7241808320955

x11 = 0.523598775598299

x12 = -34.0339204138894

x13 = -56.025068989018

x14 = -100.007366139275

x15 = 79.5870138909414

x16 = 85.870199198121

x17 = -59.1666616426078

x18 = 38.7463093942741

x19 = 38.2227106186758

x20 = -74.3510261349584

x21 = -18.3259571459405

x22 = 51.3126800086333

x23 = -17.8023583703422

x24 = 6.80678408277789

x25 = 60.7374579694027

x26 = -30.3687289847013

x27 = 9.94837673636768

x28 = -68.0678408277789

x29 = -96.342174710087

x30 = 50.789081233035

x31 = -14.6607657167524

x32 = 41.8879020478639

x33 = 79.0634151153431

x34 = 25.6563400043166

x35 = -15.1843644923507

x36 = -39.7935069454707

x37 = 13.6135681655558

x38 = 57.5958653158129

x39 = 23.0383461263252

x40 = 35.6047167406843

x41 = 60.2138591938044

x42 = 73.3038285837618

x43 = 29.3215314335047

x44 = -27.7507351067098

x45 = -61.7846555205993

x46 = 314.682864134578

x47 = -2.0943951023932

x48 = 75.9218224617533

x49 = 92.1533845053006

x50 = 88.4881930761125

x51 = -80.634211442138

x52 = -90.0589894029074

x53 = -58.6430628670095

x54 = 48.1710873550435

x55 = 4.18879020478639

x56 = 31.9395253114962

x57 = -43.4586983746588

x58 = 16.2315620435473

x59 = 97.9129710368819

x60 = -5.75958653158129

x61 = -49.7418836818384

x62 = -46.0766922526503

x63 = -24.0855436775217

x64 = -81.1578102177363

x65 = 94.7713783832921

x66 = 53.9306738866248

x67 = -71.733032256967

x68 = 82.2050077689329

x69 = 101.054563690472

x70 = 66.497044500984

x71 = -65.4498469497874

x72 = 19.8967534727354

x73 = -21.4675497995303

x74 = 44.5058959258554

x75 = 292.691715559449

x76 = -78.0162175641465

x77 = 57.0722665402146

x78 = 7.33038285837618

x79 = -8.37758040957278

x80 = -36.6519142918809

x81 = 35.081117965086

x82 = 26.1799387799149

x83 = 95.2949771588904

x84 = 22.5147473507269

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