sin5x=-√3/2 (уравнение)

Найду корень уравнения: sin5x=-√3/2

Вы ввели

              ___ 
           -\/ 3  
sin(5*x) = -------
              2   

$$\sin{\left(5 x \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$

Подробное решение

Дано уравнение
$$\sin{\left(5 x \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$5 x = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)}$$
$$5 x = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)} + \pi$$
Или
$$5 x = 2 \pi n - \frac{\pi}{3}$$
$$5 x = 2 \pi n + \frac{4 \pi}{3}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$5$$
получим ответ:
$$x_{1} = \frac{2 \pi n}{5} - \frac{\pi}{15}$$
$$x_{2} = \frac{2 \pi n}{5} + \frac{4 \pi}{15}$$

Быстрый ответ

     -pi 
x1 = ----
      15 

$$x_{1} = - \frac{\pi}{15}$$

     4*pi
x2 = ----
      15 

$$x_{2} = \frac{4 \pi}{15}$$

Сумма и произведение корней

сумма

    pi   4*pi
0 - -- + ----
    15    15 

$$\left(- \frac{\pi}{15} + 0\right) + \frac{4 \pi}{15}$$

=

pi
--
5 

$$\frac{\pi}{5}$$

произведение

  -pi  4*pi
1*----*----
   15   15 

$$\frac{4 \pi}{15} \cdot 1 \left(- \frac{\pi}{15}\right)$$

=

     2
-4*pi 
------
 225  

$$- \frac{4 \pi^{2}}{225}$$

Численный ответ

x1 = -11.7286125734019

x2 = -98.2271303022409

x3 = -47.9616478448042

x4 = 40.00294645571

x5 = 29.9498499642227

x6 = -89.6401103824288

x7 = 82.7286065445312

x8 = -27.8554548618295

x9 = 42.3067810683426

x10 = -44.1917366604964

x11 = -59.2713813977274

x12 = 38.7463093942741

x13 = 33.5103216382911

x14 = -55.710909723659

x15 = 62.4129740513172

x16 = -78.1209373192662

x17 = 80.0058929114201

x18 = -42.9350995990605

x19 = -18.0117978805815

x20 = 26.1799387799149

x21 = -58.0147443362915

x22 = -5.23598775598299

x23 = 72.4660705428046

x24 = -85.870199198121

x25 = -34.1386401690091

x26 = 83.9852436059671

x27 = 76.2359817271123

x28 = -54.2448331519838

x29 = -95.713856179369

x30 = 6.07374579694027

x31 = 94.0383400974545

x32 = 77.4926187885482

x33 = -75.8171027066337

x34 = -79.5870138909414

x35 = 60.1091394386847

x36 = 97.8082512817622

x37 = -66.8112037663429

x38 = -79.3775743807021

x39 = 18.4306769010601

x40 = 28.4837733925475

x41 = 90.2684289131467

x42 = 86.2890782185997

x43 = -25.551620249197

x44 = -24.0855436775217

x45 = 73.9321471144798

x46 = 53.8259541315051

x47 = -15.4985237577096

x48 = -81.8908485035739

x49 = -35.6047167406843

x50 = 96.342174710087

x51 = 63.8790506229925

x52 = 8.37758040957278

x53 = -64.5073691537104

x54 = 12.1474915938805

x55 = 16.1268422884276

x56 = 19.8967534727354

x57 = 9.84365698124802

x58 = -3.97935069454707

x59 = -1.67551608191456

x60 = 2.30383461263252

x61 = -21.7817090648892

x62 = -7.74926187885482

x63 = 36.2330352714023

x64 = -37.9085513533168

x65 = 52.3598775598299

x66 = 70.162235930172

x67 = -65.7640062151463

x68 = 87.7551547902749

x69 = 46.2861317628896

x70 = 5.86430628670095

x71 = 22.2005880853679

x72 = -69.5339173994541

x73 = 50.0560429471974

x74 = 104.091436588942

x75 = 66.182885235625

x76 = -14.0324471860344

x77 = 28.6932129027868

x78 = -99.6932068739161

x79 = -88.1740338107535

x80 = -45.6578132321717

x81 = -21.5722695546499

x82 = -51.7315590291119

x83 = 43.7728576400178

x84 = -68.0678408277789

x85 = -91.9439449950613

x86 = 32.2536845768552

x87 = -36.8613538021202

x88 = -71.8377520120866

x89 = -61.9940950308386

x90 = -9.21533845053006

x91 = -31.8348055563766

x92 = -0.20943951023932

x93 = 56.1297887441376

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