2sin3x=√3 (уравнение)

Найду корень уравнения: 2sin3x=√3

Вы ввели

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

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

Подробное решение

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

Разделим обе части ур-ния на 2

Ур-ние превратится в
$$\sin{\left(3 x \right)} = \frac{\sqrt{3}}{2}$$
Это ур-ние преобразуется в
$$3 x = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{3}}{2} \right)}$$
$$3 x = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{3}}{2} \right)} + \pi$$
Или
$$3 x = 2 \pi n + \frac{\pi}{3}$$
$$3 x = 2 \pi n + \frac{2 \pi}{3}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$3$$
получим ответ:
$$x_{1} = \frac{2 \pi n}{3} + \frac{\pi}{9}$$
$$x_{2} = \frac{2 \pi n}{3} + \frac{2 \pi}{9}$$

Быстрый ответ

     pi
x1 = --
     9 

$$x_{1} = \frac{\pi}{9}$$

     2*pi
x2 = ----
      9  

$$x_{2} = \frac{2 \pi}{9}$$

Сумма и произведение корней

сумма

    pi   2*pi
0 + -- + ----
    9     9  

$$\left(0 + \frac{\pi}{9}\right) + \frac{2 \pi}{9}$$

=

pi
--
3 

$$\frac{\pi}{3}$$

произведение

  pi 2*pi
1*--*----
  9   9  

$$\frac{2 \pi}{9} \cdot 1 \frac{\pi}{9}$$

=

    2
2*pi 
-----
  81 

$$\frac{2 \pi^{2}}{81}$$

Численный ответ

x1 = -93.8987137572949

x2 = -99.8328332140756

x3 = 32.1140582366957

x4 = 34.2084533390889

x5 = -95.9931088596881

x6 = -64.2281164733913

x7 = -66.3225115757845

x8 = 78.190750489346

x9 = 17.1042266695444

x10 = -83.4267382453289

x11 = -16.0570291183478

x12 = 55.1524043630208

x13 = -52.010811709431

x14 = -37.3500459926787

x15 = -26.8780704807127

x16 = 61.0865238198015

x17 = -81.3323431429358

x18 = -9.77384381116824

x19 = -91.8043186549017

x20 = -3.83972435438753

x21 = -41.538836197465

x22 = 65.6243798749868

x23 = 84.1248699461267

x24 = 40.1425727958696

x25 = 170.344134994647

x26 = 15.0098315671512

x27 = 30.0196631343025

x28 = 63.5299847725936

x29 = 92.5024503556995

x30 = 80.2851455917392

x31 = 46.774823953448

x32 = 46.4257581030492

x33 = 44.331363000656

x34 = 23.7364778271229

x35 = 42.2369678982628

x36 = 672596.835709354

x37 = -60.0393262686049

x38 = -89.7099235525085

x39 = 2.44346095279206

x40 = 71.9075651821664

x41 = 0.349065850398866

x42 = 69.8131700797732

x43 = -11.8682389135614

x44 = -57.9449311662117

x45 = -45.7276264022514

x46 = 96.6912405604859

x47 = -18.151424220741

x48 = -70.5113017805709

x49 = -75.0491578357562

x50 = -55.8505360638185

x51 = -87.6155284501153

x52 = 82.0304748437335

x53 = 74.0019602845596

x54 = 11.1701072127637

x55 = -39.4444410950718

x56 = 99.1347015132779

x57 = 52.7089434102288

x58 = -79.2379480405426

x59 = -97.7384381116825

x60 = 27.9252680319093

x61 = 67.71877497738

x62 = -43.6332312998582

x63 = 50.6145483078356

x64 = -32.8121899374934

x65 = 21.6420827247297

x66 = 88.3136601509131

x67 = -68.4169066781777

x68 = -85.5211333477222

x69 = 8.72664625997165

x70 = 701.971425152119

x71 = -62.1337213709981

x72 = -28.9724655831059

x73 = 6.63225115757845

x74 = 19.5476876223365

x75 = -49.9164166070378

x76 = -5.93411945678072

x77 = 86.2192650485199

x78 = 4.53785605518526

x79 = 94.5968454580927

x80 = 48.5201532054424

x81 = -24.4346095279206

x82 = 76.0963553869528

x83 = 90.4080552533063

x84 = -22.3402144255274

x85 = 25.8308729295161

x86 = -8.02851455917392

x87 = 38.0481776934764

x88 = -53.7561409614254

x89 = -20.2458193231342

x90 = -1.74532925199433

x91 = -35.2556508902855

x92 = -13.9626340159546

x93 = -47.8220215046446

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