корень3cosx+sinx=0 (уравнение)

Найду корень уравнения: корень3cosx+sinx=0

Вы ввели

  ___                    
\/ 3 *cos(x) + sin(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 = -63.8790506229925

x2 = 39.7935069454707

x3 = 8.37758040957278

x4 = -154.985237577096

x5 = 64.9262481741891

x6 = 49.2182849062401

x7 = -29.3215314335047

x8 = -45.0294947014537

x9 = -73.3038285837618

x10 = 74.3510261349584

x11 = 7114.66016282968

x12 = -54.4542726622231

x13 = -95.2949771588904

x14 = -79.5870138909414

x15 = -89.0117918517108

x16 = -41.8879020478639

x17 = 52.3598775598299

x18 = -16.7551608191456

x19 = 93.2005820564972

x20 = 5.23598775598299

x21 = -38.7463093942741

x22 = -67.0206432765823

x23 = 61.7846555205993

x24 = -23.0383461263252

x25 = 20.943951023932

x26 = 80.634211442138

x27 = 96.342174710087

x28 = 24.0855436775217

x29 = 14.6607657167524

x30 = 11.5191730631626

x31 = 86.9173967493176

x32 = 99.4837673636768

x33 = 27.2271363311115

x34 = -51.3126800086333

x35 = 77.4926187885482

x36 = -1.0471975511966

x37 = -76.4454212373516

x38 = -92.1533845053006

x39 = -7.33038285837618

x40 = 17.8023583703422

x41 = -4.18879020478639

x42 = -35.6047167406843

x43 = -13.6135681655558

x44 = -10.471975511966

x45 = 68.0678408277789

x46 = -19.8967534727354

x47 = 36.6519142918809

x48 = 58.6430628670095

x49 = -57.5958653158129

x50 = -32.4631240870945

x51 = -82.7286065445312

x52 = 83.7758040957278

x53 = 102.625360017267

x54 = 30.3687289847013

x55 = 90.0589894029074

x56 = -60.7374579694027

x57 = 55.5014702134197

x58 = 46.0766922526503

x59 = -70.162235930172

x60 = 2.0943951023932

x61 = 33.5103216382911

x62 = 71.2094334813686

x63 = 42.9350995990605

x64 = -85.870199198121

x65 = -98.4365698124802

x66 = -48.1710873550435

x67 = -26.1799387799149

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