sin(3x)=-1/2 (уравнение)

Найду корень уравнения: sin(3x)=-1/2

Вы ввели

sin(3*x) = -1/2

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

Подробное решение

Дано уравнение
$$\sin{\left(3 x \right)} = - \frac{1}{2}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$3 x = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{2} \right)}$$
$$3 x = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{2} \right)} + \pi$$
Или
$$3 x = 2 \pi n - \frac{\pi}{6}$$
$$3 x = 2 \pi n + \frac{7 \pi}{6}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$3$$
получим ответ:
$$x_{1} = \frac{2 \pi n}{3} - \frac{\pi}{18}$$
$$x_{2} = \frac{2 \pi n}{3} + \frac{7 \pi}{18}$$

Быстрый ответ

     -pi 
x1 = ----
      18 

$$x_{1} = - \frac{\pi}{18}$$

     7*pi
x2 = ----
      18 

$$x_{2} = \frac{7 \pi}{18}$$

Численный ответ

x1 = 33.3357887130917

x2 = -46.2512251778497

x3 = 52.1853446346305

x4 = 28.4488668075076

x5 = -65.7989128001862

x6 = -42.0624349730633

x7 = 26.3544717051144

x8 = -61.6101225953998

x9 = -31.5904594610974

x10 = -59.5157274930066

x11 = 83.6012711705284

x12 = -75.5727566113545

x13 = -23.9110107523223

x14 = 17.9768912955416

x15 = 87.7900613753148

x16 = 85.6956662729216

x17 = 39.6189740202713

x18 = 61.9591884457987

x19 = 89.884456477708

x20 = -74.176493209759

x21 = -90.2335223281068

x22 = -33.6848545634906

x23 = 45.9021593274509

x24 = 68.2423737529783

x25 = 74.5255590601579

x26 = 30.5432619099008

x27 = -11.3446401379631

x28 = -98.6111027376796

x29 = -92.3279174305

x30 = -26.0054058547155

x31 = 43.8077642250577

x32 = -81.8559419185341

x33 = -69.9877030049726

x34 = -72.0820981073658

x35 = -21.8166156499291

x36 = -7.15584993317675

x37 = 1.91986217719376

x38 = 100.356431989674

x39 = 54.2797397370236

x40 = 47.9965544298441

x41 = -37.873644768277

x42 = -16.929693744345

x43 = -15.5334303427495

x44 = 76.6199541625511

x45 = -4.36332312998582

x46 = 12.3918376891597

x47 = 72.4311639577647

x48 = -83.9503370209273

x49 = 8.20304748437335

x50 = -57.4213323906134

x51 = 22.165681500328

x52 = -35.7792496658838

x53 = -48.3456202802429

x54 = -77.6671517137477

x55 = 15.8824961931484

x56 = -63.704517697793

x57 = 56.3741348394168

x58 = -44.1568300754565

x59 = -28.0998009571087

x60 = -79.7615468161409

x61 = 10.2974425867665

x62 = 66.1479786505851

x63 = -54.6288055874225

x64 = -39.9680398706701

x65 = 96.1676417848876

x66 = 24.2600766027212

x67 = -0.174532925199433

x68 = -88.1391272257137

x69 = 20.0712863979348

x70 = 94.0732466824944

x71 = -2.26892802759263

x72 = 4.01425727958696

x73 = -51.1381470834339

x74 = 91.9788515801012

x75 = -86.0447321233204

x76 = -17.6278254451427

x77 = 646.2954220135

x78 = -67.8933079025794

x79 = 32.637657012294

x80 = 98.2620368872808

x81 = 6.10865238198015

x82 = -19.7222205475359

x83 = -13.4390352403563

x84 = 59.8647933434055

x85 = 64.0535835481919

x86 = 70.3367688553715

x87 = 77.3180858633488

x88 = 50.0909495322373

x89 = 41.7133691226645

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