sinx=-√3/2 (уравнение)

Найду корень уравнения: sinx=-√3/2

Вы ввели

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

$$\sin{\left(x \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
- 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
$$x = 2 \pi n - \frac{\pi}{3}$$
$$x = 2 \pi n + \frac{4 \pi}{3}$$
, где n - любое целое число

Сумма и произведение корней

сумма

    pi   4*pi
0 - -- + ----
    3     3  

$$\left(- \frac{\pi}{3} + 0\right) + \frac{4 \pi}{3}$$

=

pi

$$\pi$$

произведение

  -pi  4*pi
1*----*----
   3    3  

$$\frac{4 \pi}{3} \cdot 1 \left(- \frac{\pi}{3}\right)$$

=

     2
-4*pi 
------
  9   

$$- \frac{4 \pi^{2}}{9}$$

Быстрый ответ

     -pi 
x1 = ----
      3  

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

     4*pi
x2 = ----
      3  

$$x_{2} = \frac{4 \pi}{3}$$

Численный ответ

x1 = -20.943951023932

x2 = -63.8790506229925

x3 = -114.144533080429

x4 = 49.2182849062401

x5 = 74.3510261349584

x6 = -101.57816246607

x7 = -45.0294947014537

x8 = -46.0766922526503

x9 = -33.5103216382911

x10 = 67.0206432765823

x11 = -95.2949771588904

x12 = 60.7374579694027

x13 = -89.0117918517108

x14 = -83.7758040957278

x15 = 23.0383461263252

x16 = -27.2271363311115

x17 = 35.6047167406843

x18 = -38.7463093942741

x19 = 93.2005820564972

x20 = 5.23598775598299

x21 = 61.7846555205993

x22 = -1559.27715373173

x23 = -96.342174710087

x24 = -52.3598775598299

x25 = -11851.1346868919

x26 = 16.7551608191456

x27 = -14.6607657167524

x28 = 80.634211442138

x29 = 29.3215314335047

x30 = 11.5191730631626

x31 = 86.9173967493176

x32 = 24.0855436775217

x33 = 41.8879020478639

x34 = 99.4837673636768

x35 = 98.4365698124802

x36 = -51.3126800086333

x37 = -1.0471975511966

x38 = -76.4454212373516

x39 = -7.33038285837618

x40 = -2.0943951023932

x41 = 10.471975511966

x42 = 17.8023583703422

x43 = 92.1533845053006

x44 = -13.6135681655558

x45 = -5606.69568910658

x46 = 68.0678408277789

x47 = -19.8967534727354

x48 = -39.7935069454707

x49 = -77.4926187885482

x50 = 36.6519142918809

x51 = -8.37758040957278

x52 = 79.5870138909414

x53 = 85.870199198121

x54 = -71.2094334813686

x55 = -57.5958653158129

x56 = -32.4631240870945

x57 = -82.7286065445312

x58 = -90.0589894029074

x59 = -58.6430628670095

x60 = 4.18879020478639

x61 = 48.1710873550435

x62 = 30.3687289847013

x63 = 393.746279249921

x64 = 55.5014702134197

x65 = -64.9262481741891

x66 = -70.162235930172

x67 = 42.9350995990605

x68 = 54.4542726622231

x69 = 73.3038285837618

x70 = -26.1799387799149

x71 = -151.843644923507

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