sin(x)=✓3/2 (уравнение)

Найду корень уравнения: sin(x)=✓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
-- + ----
3     3  

$$\frac{\pi}{3} + \frac{2 \pi}{3}$$

=

pi

$$\pi$$

произведение

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

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

=

    2
2*pi 
-----
  9  

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

Численный ответ

x1 = -17.8023583703422

x2 = -49.2182849062401

x3 = 89.0117918517108

x4 = -74.3510261349584

x5 = -73.3038285837618

x6 = -42.9350995990605

x7 = -79.5870138909414

x8 = 96.342174710087

x9 = 240.855436775217

x10 = 33.5103216382911

x11 = -67.0206432765823

x12 = 101.57816246607

x13 = 19.8967534727354

x14 = -29.3215314335047

x15 = -54.4542726622231

x16 = 146.607657167524

x17 = -30.3687289847013

x18 = 39.7935069454707

x19 = 95.2949771588904

x20 = -68.0678408277789

x21 = -98.4365698124802

x22 = 71.2094334813686

x23 = 26.1799387799149

x24 = 2.0943951023932

x25 = 14.6607657167524

x26 = 64.9262481741891

x27 = 209.43951023932

x28 = -24.0855436775217

x29 = 46.0766922526503

x30 = -36.6519142918809

x31 = -85.870199198121

x32 = -4.18879020478639

x33 = -35.6047167406843

x34 = 1.0471975511966

x35 = 7.33038285837618

x36 = 83.7758040957278

x37 = 52.3598775598299

x38 = 57.5958653158129

x39 = 27.2271363311115

x40 = 195.825942073764

x41 = 32.4631240870945

x42 = -92.1533845053006

x43 = 76.4454212373516

x44 = 82.7286065445312

x45 = -48.1710873550435

x46 = 8.37758040957278

x47 = 170.693200845045

x48 = -99.4837673636768

x49 = -23.0383461263252

x50 = -16.7551608191456

x51 = -520.457182944709

x52 = 51.3126800086333

x53 = -112.050137978036

x54 = -104.71975511966

x55 = -61.7846555205993

x56 = -11.5191730631626

x57 = -93.2005820564972

x58 = -5.23598775598299

x59 = 77.4926187885482

x60 = 58.6430628670095

x61 = 1188.56922060814

x62 = -41.8879020478639

x63 = -6607.81654805053

x64 = 38.7463093942741

x65 = -10.471975511966

x66 = -60.7374579694027

x67 = 45.0294947014537

x68 = 63.8790506229925

x69 = 13.6135681655558

x70 = 944.572191179331

x71 = -80.634211442138

x72 = -613.657765001206

x73 = 90.0589894029074

x74 = 20.943951023932

x75 = -55.5014702134197

x76 = 70.162235930172

x77 = -86.9173967493176

График