√3sin(x)+cos(x)=0 (уравнение)

Найду корень уравнения: √3sin(x)+cos(x)=0

Вы ввели

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

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

Подробное решение

Дано уравнение
$$\sqrt{3} \sin{\left(x \right)} + \cos{\left(x \right)} = 0$$
преобразуем:
$$\frac{\sqrt{3} \sin{\left(x \right)}}{\cos{\left(x \right)}} = -1$$
или
$$\sqrt{3} \tan{\left(x \right)} = -1$$
- это простейшее тригонометрическое ур-ние

Разделим обе части ур-ния на sqrt(3)

Ур-ние превратится в
$$\tan{\left(x \right)} = \frac{\sqrt{3}}{3}$$
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{atan}{\left(\frac{\sqrt{3}}{3} \right)}$$
Или
$$x = \pi n + \frac{\pi}{6}$$
, где n - любое целое число

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 = 37.1755130674792

x2 = 74.8746249105567

x3 = -101.054563690472

x4 = -66.497044500984

x5 = 131.423292675173

x6 = 52.8834763354282

x7 = 81.1578102177363

x8 = -60.2138591938044

x9 = -94.7713783832921

x10 = -50.789081233035

x11 = 24.60914245312

x12 = 100.007366139275

x13 = -19.3731546971371

x14 = 68.5914396033772

x15 = -914.727060970228

x16 = 65.4498469497874

x17 = 43.4586983746588

x18 = 21.4675497995303

x19 = 40.317105721069

x20 = -47.6474885794452

x21 = -72.7802298081635

x22 = -0.523598775598299

x23 = -75.9218224617533

x24 = 34.0339204138894

x25 = -9.94837673636768

x26 = 30.8923277602996

x27 = 18.3259571459405

x28 = -79.0634151153431

x29 = 15.1843644923507

x30 = -63.3554518473942

x31 = -85.3466004225227

x32 = 59.1666616426078

x33 = -38.2227106186758

x34 = 93.7241808320955

x35 = 71.733032256967

x36 = -22.5147473507269

x37 = -25.6563400043166

x38 = -31.9395253114962

x39 = -35.081117965086

x40 = 2.61799387799149

x41 = -69.6386371545737

x42 = 12.0427718387609

x43 = 78.0162175641465

x44 = 87.4409955249159

x45 = -57.0722665402146

x46 = -97.9129710368819

x47 = -16.2315620435473

x48 = -13.0899693899575

x49 = 46.6002910282486

x50 = -82.2050077689329

x51 = -91.6297857297023

x52 = 62.3082542961976

x53 = 49.7418836818384

x54 = -28.7979326579064

x55 = -3.66519142918809

x56 = 56.025068989018

x57 = 5.75958653158129

x58 = -53.9306738866248

x59 = -6.80678408277789

x60 = 84.2994028713261

x61 = -88.4881930761125

x62 = 96.8657734856853

x63 = -41.3643032722656

x64 = 8.90117918517108

x65 = 27.7507351067098

x66 = -44.5058959258554

x67 = 90.5825881785057

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