sqrt(3)*sin(2*x)+3*cos(2*x)=0 (уравнение)

Найду корень уравнения: sqrt(3)*sin(2*x)+3*cos(2*x)=0

Вы ввели

  ___                          
\/ 3 *sin(2*x) + 3*cos(2*x) = 0

$$\sqrt{3} \sin{\left(2 x \right)} + 3 \cos{\left(2 x \right)} = 0$$

Подробное решение

Дано уравнение
$$\sqrt{3} \sin{\left(2 x \right)} + 3 \cos{\left(2 x \right)} = 0$$
преобразуем:
$$\frac{\sqrt{3} \sin{\left(2 x \right)}}{\cos{\left(2 x \right)}} = -3$$
или
$$\sqrt{3} \tan{\left(2 x \right)} = -3$$
- это простейшее тригонометрическое ур-ние

Разделим обе части ур-ния на sqrt(3)

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

Быстрый ответ

     -pi 
x1 = ----
      6  

$$x_{1} = - \frac{\pi}{6}$$

Сумма и произведение корней

сумма

    pi
0 - --
    6 

$$- \frac{\pi}{6} + 0$$

=

-pi 
----
 6  

$$- \frac{\pi}{6}$$

произведение

  -pi 
1*----
   6  

$$1 \left(- \frac{\pi}{6}\right)$$

=

-pi 
----
 6  

$$- \frac{\pi}{6}$$

Численный ответ

x1 = 82.7286065445312

x2 = -16.2315620435473

x3 = 71.733032256967

x4 = -55.5014702134197

x5 = -38.2227106186758

x6 = -31.9395253114962

x7 = 38.7463093942741

x8 = 27.7507351067098

x9 = 84.2994028713261

x10 = 90.5825881785057

x11 = 13.6135681655558

x12 = 1279.67540756224

x13 = -99.4837673636768

x14 = -91.6297857297023

x15 = -96.342174710087

x16 = 26.1799387799149

x17 = -33.5103216382911

x18 = -25.6563400043166

x19 = -5.23598775598299

x20 = 68.5914396033772

x21 = -28.7979326579064

x22 = 48.1710873550435

x23 = -90.0589894029074

x24 = -426.209403337015

x25 = -30.3687289847013

x26 = -75.9218224617533

x27 = -47.6474885794452

x28 = -44.5058959258554

x29 = 34.0339204138894

x30 = -88.4881930761125

x31 = -52.3598775598299

x32 = 10.471975511966

x33 = 62.3082542961976

x34 = 35.6047167406843

x35 = -3.66519142918809

x36 = 54.4542726622231

x37 = -22.5147473507269

x38 = -0.523598775598299

x39 = -63.3554518473942

x40 = 12.0427718387609

x41 = 98.4365698124802

x42 = -39.7935069454707

x43 = -74.3510261349584

x44 = 93.7241808320955

x45 = -97.9129710368819

x46 = -24.0855436775217

x47 = 16.7551608191456

x48 = 2.61799387799149

x49 = -85.3466004225227

x50 = 63.8790506229925

x51 = -60.2138591938044

x52 = 100.007366139275

x53 = -8.37758040957278

x54 = 19.8967534727354

x55 = 85.870199198121

x56 = -61.7846555205993

x57 = 24.60914245312

x58 = 60.7374579694027

x59 = 41.8879020478639

x60 = -53.9306738866248

x61 = -66.497044500984

x62 = 21.4675497995303

x63 = -46.0766922526503

x64 = -82.2050077689329

x65 = 56.025068989018

x66 = 5.75958653158129

x67 = 78.0162175641465

x68 = -77.4926187885482

x69 = 70.162235930172

x70 = 101.57816246607

x71 = -2.0943951023932

x72 = 4.18879020478639

x73 = 46.6002910282486

x74 = 76.4454212373516

x75 = -41.3643032722656

x76 = 40.317105721069

x77 = -69.6386371545737

x78 = -11.5191730631626

x79 = 32.4631240870945

x80 = -17.8023583703422

x81 = 18.3259571459405

x82 = 57.5958653158129

x83 = -68.0678408277789

x84 = 49.7418836818384

x85 = -19.3731546971371

x86 = -9.94837673636768

x87 = 92.1533845053006

x88 = -83.7758040957278

x89 = 79.5870138909414

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