sinx+√3cosx=0 (уравнение)

Найду корень уравнения: sinx+√3cosx=0

Вы ввели

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

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

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} + \sqrt{3} \cos{\left(x \right)} = 0$$
преобразуем:
$$\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} = - \sqrt{3}$$
или
$$\tan{\left(x \right)} = - \sqrt{3}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{atan}{\left(\sqrt{3} \right)}$$
Или
$$x = \pi n + \frac{\pi}{3}$$
, где n - любое целое число

Быстрый ответ

     -pi 
x1 = ----
      3  

$$x_{1} = - \frac{\pi}{3}$$

Сумма и произведение корней

сумма

    pi
0 - --
    3 

$$- \frac{\pi}{3} + 0$$

=

-pi 
----
 3  

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

произведение

  -pi 
1*----
   3  

$$1 \left(- \frac{\pi}{3}\right)$$

=

-pi 
----
 3  

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

Численный ответ

x1 = 5.23598775598299

x2 = 77.4926187885482

x3 = 55.5014702134197

x4 = 58.6430628670095

x5 = -10.471975511966

x6 = 33.5103216382911

x7 = -76.4454212373516

x8 = -79.5870138909414

x9 = -45.0294947014537

x10 = -13.6135681655558

x11 = -19.8967534727354

x12 = -67.0206432765823

x13 = -92.1533845053006

x14 = -4.18879020478639

x15 = 8.37758040957278

x16 = -82.7286065445312

x17 = -1.0471975511966

x18 = 96.342174710087

x19 = -51.3126800086333

x20 = -154.985237577096

x21 = -85.870199198121

x22 = 14.6607657167524

x23 = -32.4631240870945

x24 = 74.3510261349584

x25 = 93.2005820564972

x26 = 30.3687289847013

x27 = 17.8023583703422

x28 = -70.162235930172

x29 = -23.0383461263252

x30 = 49.2182849062401

x31 = -38.7463093942741

x32 = 90.0589894029074

x33 = -29.3215314335047

x34 = 52.3598775598299

x35 = 86.9173967493176

x36 = -63.8790506229925

x37 = -54.4542726622231

x38 = 46.0766922526503

x39 = 36.6519142918809

x40 = 27.2271363311115

x41 = 7114.66016282968

x42 = -48.1710873550435

x43 = 39.7935069454707

x44 = 24.0855436775217

x45 = -95.2949771588904

x46 = -35.6047167406843

x47 = -73.3038285837618

x48 = -7.33038285837618

x49 = 80.634211442138

x50 = 61.7846555205993

x51 = -16.7551608191456

x52 = 42.9350995990605

x53 = -60.7374579694027

x54 = 68.0678408277789

x55 = 20.943951023932

x56 = 11.5191730631626

x57 = 99.4837673636768

x58 = -98.4365698124802

x59 = -26.1799387799149

x60 = 64.9262481741891

x61 = -89.0117918517108

x62 = -57.5958653158129

x63 = -41.8879020478639

x64 = 102.625360017267

x65 = 71.2094334813686

x66 = 2.0943951023932

x67 = 83.7758040957278

График