tg5x+√3=0 (уравнение)

Найду корень уравнения: tg5x+√3=0

Вы ввели

             ___    
tan(5*x) + \/ 3  = 0

$$\tan{\left(5 x \right)} + \sqrt{3} = 0$$

Подробное решение

Дано уравнение
$$\tan{\left(5 x \right)} + \sqrt{3} = 0$$
- это простейшее тригонометрическое ур-ние

Перенесём sqrt(3) в правую часть ур-ния

с изменением знака при sqrt(3)

Получим:
$$\tan{\left(5 x \right)} = - \sqrt{3}$$
Это ур-ние преобразуется в
$$5 x = \pi n + \operatorname{atan}{\left(- \sqrt{3} \right)}$$
Или
$$5 x = \pi n - \frac{\pi}{3}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$5$$
получим ответ:
$$x_{1} = \frac{\pi n}{5} - \frac{\pi}{15}$$

Быстрый ответ

     -pi 
x1 = ----
      15 

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

Сумма и произведение корней

сумма

    pi
0 - --
    15

$$- \frac{\pi}{15} + 0$$

=

-pi 
----
 15 

$$- \frac{\pi}{15}$$

произведение

  -pi 
1*----
   15 

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

=

-pi 
----
 15 

$$- \frac{\pi}{15}$$

Численный ответ

x1 = 63.8790506229925

x2 = -22.2005880853679

x3 = 33.7197611485304

x4 = 58.2241838465308

x5 = -29.7404104539834

x6 = -0.20943951023932

x7 = 24.2949831877611

x8 = -83.7758040957278

x9 = 70.162235930172

x10 = 94.0383400974545

x11 = -3.97935069454707

x12 = 51.9409985393512

x13 = 53.8259541315051

x14 = -81.8908485035739

x15 = 99.6932068739161

x16 = -12.1474915938805

x17 = -93.8289005872152

x18 = -7.74926187885482

x19 = 75.8171027066337

x20 = -76.2359817271123

x21 = 95.9232956896084

x22 = 28.0648943720688

x23 = 90.2684289131467

x24 = -73.7227076042405

x25 = -17.8023583703422

x26 = 68.2772803380182

x27 = 50.0560429471974

x28 = -51.7315590291119

x29 = -88.1740338107535

x30 = 16.1268422884276

x31 = -49.8466034369581

x32 = 80.2153324216594

x33 = 31.8348055563766

x34 = -68.0678408277789

x35 = -37.9085513533168

x36 = 61.9940950308386

x37 = 29.9498499642227

x38 = 72.0471915223259

x39 = 6.07374579694027

x40 = 41.8879020478639

x41 = 36.2330352714023

x42 = -80.0058929114201

x43 = 43.7728576400178

x44 = 40.00294645571

x45 = 14.2418866962737

x46 = -15.9174027781883

x47 = -39.7935069454707

x48 = -44.1917366604964

x49 = 1.67551608191456

x50 = -91.9439449950613

x51 = -42.3067810683426

x52 = 55.710909723659

x53 = 21.7817090648892

x54 = 73.9321471144798

x55 = -47.9616478448042

x56 = 97.8082512817622

x57 = -78.1209373192662

x58 = 9.84365698124802

x59 = 7.95870138909414

x60 = 77.7020582987875

x61 = -86.2890782185997

x62 = -58.0147443362915

x63 = -61.7846555205993

x64 = -54.2448331519838

x65 = -66.182885235625

x66 = -95.713856179369

x67 = -2.0943951023932

x68 = 92.1533845053006

x69 = 18.0117978805815

x70 = -100.112085894395

x71 = -25.9704992696756

x72 = 46.2861317628896

x73 = 48.1710873550435

x74 = 60.1091394386847

x75 = 4.18879020478639

x76 = -10.2625360017267

x77 = -27.8554548618295

x78 = -36.023595761163

x79 = 83.9852436059671

x80 = -46.0766922526503

x81 = -24.0855436775217

x82 = -98.2271303022409

x83 = -64.2979296434711

x84 = -5.86430628670095

x85 = -31.6253660461373

x86 = 19.8967534727354

x87 = -20.315632493214

x88 = -71.8377520120866

x89 = 65.7640062151463

x90 = -69.9527964199327

x91 = 11.7286125734019

x92 = 26.1799387799149

x93 = -14.0324471860344

x94 = 87.7551547902749

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