2sinx=√3 (уравнение)

Найду корень уравнения: 2sinx=√3

Вы ввели

             ___
2*sin(x) = \/ 3 

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

Подробное решение

Дано уравнение
$$2 \sin{\left(x \right)} = \sqrt{3}$$
- это простейшее тригонометрическое ур-ние

Разделим обе части ур-ния на 2

Ур-ние превратится в
$$\sin{\left(x \right)} = \frac{\sqrt{3}}{2}$$
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{3}}{2} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{3}}{2} \right)} + \pi$$
Или
$$x = 2 \pi n + \frac{\pi}{3}$$
$$x = 2 \pi n + \frac{2 \pi}{3}$$
, где n - любое целое число

Быстрый ответ

     pi
x1 = --
     3 

$$x_{1} = \frac{\pi}{3}$$

     2*pi
x2 = ----
      3  

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

Сумма и произведение корней

сумма

    pi   2*pi
0 + -- + ----
    3     3  

$$\left(0 + \frac{\pi}{3}\right) + \frac{2 \pi}{3}$$

=

pi

$$\pi$$

произведение

  pi 2*pi
1*--*----
  3   3  

$$\frac{2 \pi}{3} \cdot 1 \frac{\pi}{3}$$

=

    2
2*pi 
-----
  9  

$$\frac{2 \pi^{2}}{9}$$

Численный ответ

x1 = 83.7758040957278

x2 = 8.37758040957278

x3 = -112.050137978036

x4 = 64.9262481741891

x5 = 63.8790506229925

x6 = -54.4542726622231

x7 = -79.5870138909414

x8 = 70.162235930172

x9 = 45.0294947014537

x10 = 14.6607657167524

x11 = -520.457182944709

x12 = 38.7463093942741

x13 = 101.57816246607

x14 = 46.0766922526503

x15 = -74.3510261349584

x16 = 71.2094334813686

x17 = 170.693200845045

x18 = -29.3215314335047

x19 = -613.657765001206

x20 = 51.3126800086333

x21 = 195.825942073764

x22 = -17.8023583703422

x23 = -5.23598775598299

x24 = 52.3598775598299

x25 = -30.3687289847013

x26 = -67.0206432765823

x27 = -23.0383461263252

x28 = 209.43951023932

x29 = -68.0678408277789

x30 = 96.342174710087

x31 = 82.7286065445312

x32 = 90.0589894029074

x33 = -60.7374579694027

x34 = 13.6135681655558

x35 = -49.2182849062401

x36 = -48.1710873550435

x37 = 1188.56922060814

x38 = 57.5958653158129

x39 = -6607.81654805053

x40 = -73.3038285837618

x41 = 32.4631240870945

x42 = -11.5191730631626

x43 = -61.7846555205993

x44 = -92.1533845053006

x45 = -4.18879020478639

x46 = -35.6047167406843

x47 = 240.855436775217

x48 = -80.634211442138

x49 = 76.4454212373516

x50 = -55.5014702134197

x51 = -42.9350995990605

x52 = 2.0943951023932

x53 = 33.5103216382911

x54 = -98.4365698124802

x55 = 39.7935069454707

x56 = -24.0855436775217

x57 = -41.8879020478639

x58 = -16.7551608191456

x59 = 20.943951023932

x60 = 1.0471975511966

x61 = 19.8967534727354

x62 = 27.2271363311115

x63 = 77.4926187885482

x64 = 89.0117918517108

x65 = -10.471975511966

x66 = -99.4837673636768

x67 = 146.607657167524

x68 = 7.33038285837618

x69 = -36.6519142918809

x70 = 58.6430628670095

x71 = 944.572191179331

x72 = 26.1799387799149

x73 = -93.2005820564972

x74 = -104.71975511966

x75 = -85.870199198121

x76 = -86.9173967493176

x77 = 95.2949771588904

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