sinx=√3/2 (уравнение)

Найду корень уравнения: sinx=√3/2

Вы ввели

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

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

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = \frac{\sqrt{3}}{2}$$
- это простейшее тригонометрическое ур-ние
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 = -23.0383461263252

x2 = 82.7286065445312

x3 = -55.5014702134197

x4 = 38.7463093942741

x5 = 83.7758040957278

x6 = 33.5103216382911

x7 = 146.607657167524

x8 = 95.2949771588904

x9 = 13.6135681655558

x10 = -42.9350995990605

x11 = -104.71975511966

x12 = -99.4837673636768

x13 = -16.7551608191456

x14 = 26.1799387799149

x15 = -5.23598775598299

x16 = -85.870199198121

x17 = -613.657765001206

x18 = 39.7935069454707

x19 = 195.825942073764

x20 = -30.3687289847013

x21 = 27.2271363311115

x22 = 170.693200845045

x23 = -80.634211442138

x24 = 2.0943951023932

x25 = 77.4926187885482

x26 = -79.5870138909414

x27 = 7.33038285837618

x28 = -48.1710873550435

x29 = -49.2182849062401

x30 = 1188.56922060814

x31 = -92.1533845053006

x32 = 71.2094334813686

x33 = 944.572191179331

x34 = -4.18879020478639

x35 = -98.4365698124802

x36 = -74.3510261349584

x37 = -520.457182944709

x38 = -10.471975511966

x39 = -24.0855436775217

x40 = 90.0589894029074

x41 = -6607.81654805053

x42 = -35.6047167406843

x43 = 96.342174710087

x44 = 63.8790506229925

x45 = 8.37758040957278

x46 = 1.0471975511966

x47 = -86.9173967493176

x48 = 51.3126800086333

x49 = 19.8967534727354

x50 = 209.43951023932

x51 = -36.6519142918809

x52 = -61.7846555205993

x53 = -41.8879020478639

x54 = -54.4542726622231

x55 = -29.3215314335047

x56 = 52.3598775598299

x57 = 70.162235930172

x58 = 101.57816246607

x59 = -112.050137978036

x60 = -73.3038285837618

x61 = 76.4454212373516

x62 = 58.6430628670095

x63 = -67.0206432765823

x64 = -11.5191730631626

x65 = 32.4631240870945

x66 = -17.8023583703422

x67 = 57.5958653158129

x68 = 20.943951023932

x69 = -68.0678408277789

x70 = 240.855436775217

x71 = -93.2005820564972

x72 = 89.0117918517108

x73 = 46.0766922526503

x74 = 45.0294947014537

x75 = 64.9262481741891

x76 = 14.6607657167524

x77 = -60.7374579694027

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