sin(4*x) - sqrt(3)/2 = 0 (уравнение)

Найду корень уравнения: sin(4*x) - sqrt(3)/2 = 0

Вы ввели

             ___    
           \/ 3     
sin(4*x) - ----- = 0
             2      

$$\sin{\left(4 x \right)} - \frac{\sqrt{3}}{2} = 0$$

Подробное решение

Дано уравнение
$$\sin{\left(4 x \right)} - \frac{\sqrt{3}}{2} = 0$$
- это простейшее тригонометрическое ур-ние

Перенесём -sqrt(3)/2 в правую часть ур-ния

с изменением знака при -sqrt(3)/2

Получим:
$$\sin{\left(4 x \right)} - \frac{\sqrt{3}}{2} + \frac{\sqrt{3}}{2} = \frac{\sqrt{3}}{2}$$
Это ур-ние преобразуется в
$$4 x = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{3}}{2} \right)}$$
$$4 x = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{3}}{2} \right)} + \pi$$
Или
$$4 x = 2 \pi n + \frac{\pi}{3}$$
$$4 x = 2 \pi n + \frac{2 \pi}{3}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$4$$
получим ответ:
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{12}$$
$$x_{2} = \frac{\pi n}{2} + \frac{\pi}{6}$$

Быстрый ответ

     pi
x1 = --
     12

$$x_{1} = \frac{\pi}{12}$$

     pi
x2 = --
     6 

$$x_{2} = \frac{\pi}{6}$$

Численный ответ

x1 = 50.5272818452358

x2 = 8.11578102177363

x3 = 3.66519142918809

x4 = -13.8753675533549

x5 = 36.3901149040818

x6 = 2.0943951023932

x7 = 91.3679863419031

x8 = 94.5095789954929

x9 = -71.733032256967

x10 = 17.8023583703422

x11 = 91.6297857297023

x12 = -12.0427718387609

x13 = -37.4373124552784

x14 = -35.8665161284835

x15 = 171.478599008443

x16 = -95.5567765466895

x17 = 30.1069295969022

x18 = -79.8488132787406

x19 = -4.18879020478639

x20 = -5.75958653158129

x21 = -87.7027949127151

x22 = 72.5184304203644

x23 = 16.2315620435473

x24 = -40.317105721069

x25 = -41.8879020478639

x26 = -34.0339204138894

x27 = -65.7116463375865

x28 = 61.7846555205993

x29 = -19.8967534727354

x30 = -81.4196096055355

x31 = 38.2227106186758

x32 = -84.2994028713261

x33 = 0.261799387799149

x34 = -73.565627971561

x35 = 74.0892267471593

x36 = 82.2050077689329

x37 = -49.7418836818384

x38 = -48.1710873550435

x39 = -21.7293491873294

x40 = -56.025068989018

x41 = -59.4284610304069

x42 = 44.2440965380563

x43 = -70.162235930172

x44 = 14.3989663289532

x45 = 53.9306738866248

x46 = -56.2868683768171

x47 = 6.54498469497874

x48 = 39.7935069454707

x49 = 97.9129710368819

x50 = 75.9218224617533

x51 = -18.3259571459405

x52 = -26.1799387799149

x53 = 90.0589894029074

x54 = -100.007366139275

x55 = 69.3768377667746

x56 = -57.857664703612

x57 = -27.7507351067098

x58 = 28.5361332701073

x59 = 24.0855436775217

x60 = 31.9395253114962

x61 = -63.8790506229925

x62 = 96.0803753222878

x63 = 25.6563400043166

x64 = -62.3082542961976

x65 = -43.720497762458

x66 = -15.4461638801498

x67 = 83.7758040957278

x68 = 52.0980781720307

x69 = -93.7241808320955

x70 = 68.0678408277789

x71 = 64.9262481741891

x72 = 46.0766922526503

x73 = 60.2138591938044

x74 = -51.5744793964324

x75 = 86.9173967493176

x76 = 88.2263936883134

x77 = -85.870199198121

x78 = 58.3812634792103

x79 = -7.59218224617533

x80 = -78.0162175641465

x81 = -2167.43713158916

x82 = 9.94837673636768

x83 = 66.2352451131848

x84 = 47.6474885794452

x85 = -29.5833308213039

x86 = 22.2529479629277

x87 = 80.3724120543389

x88 = 5.23598775598299

x89 = -92.1533845053006

x90 = -31.1541271480988

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