cos2x=-√3/2 (уравнение)

Найду корень уравнения: cos2x=-√3/2

Вы ввели

              ___ 
           -\/ 3  
cos(2*x) = -------
              2   

$$\cos{\left(2 x \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$

Подробное решение

Дано уравнение
$$\cos{\left(2 x \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$2 x = \pi n + \operatorname{acos}{\left(- \frac{\sqrt{3}}{2} \right)}$$
$$2 x = \pi n - \pi + \operatorname{acos}{\left(- \frac{\sqrt{3}}{2} \right)}$$
Или
$$2 x = \pi n + \frac{5 \pi}{6}$$
$$2 x = \pi n - \frac{\pi}{6}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$2$$
получим ответ:
$$x_{1} = \frac{\pi n}{2} + \frac{5 \pi}{12}$$
$$x_{2} = \frac{\pi n}{2} - \frac{\pi}{12}$$

Сумма и произведение корней

сумма

    5*pi   7*pi
0 + ---- + ----
     12     12 

$$\left(0 + \frac{5 \pi}{12}\right) + \frac{7 \pi}{12}$$

=

pi

$$\pi$$

произведение

  5*pi 7*pi
1*----*----
   12   12 

$$\frac{7 \pi}{12} \cdot 1 \cdot \frac{5 \pi}{12}$$

=

     2
35*pi 
------
 144  

$$\frac{35 \pi^{2}}{144}$$

Быстрый ответ

     5*pi
x1 = ----
      12 

$$x_{1} = \frac{5 \pi}{12}$$

     7*pi
x2 = ----
      12 

$$x_{2} = \frac{7 \pi}{12}$$

Численный ответ

x1 = -45.2912940892529

x2 = 1.83259571459405

x3 = -39.5317075576716

x4 = -23.8237442897226

x5 = -32.7249234748937

x6 = 58.3812634792103

x7 = 8.11578102177363

x8 = -70.9476340935695

x9 = 26.4417381677141

x10 = -1899.35455848283

x11 = 17.0169602069447

x12 = 45.8148928648512

x13 = 52.0980781720307

x14 = -26.4417381677141

x15 = -1.30899693899575

x16 = 48.4328867428426

x17 = 80.3724120543389

x18 = -76.7072206251508

x19 = 54.7160720500222

x20 = 89.7971900151083

x21 = 82.9904059323304

x22 = 92.4151838930998

x23 = 10.7337748997651

x24 = 4.45058959258554

x25 = 23.8237442897226

x26 = 3925.15822127265

x27 = -52.0980781720307

x28 = -33.248522250492

x29 = 60.9992573572018

x30 = -82.9904059323304

x31 = 86.1319985859202

x32 = 42.1497014356631

x33 = -4.45058959258554

x34 = -11.2573736753634

x35 = -83.5140047079287

x36 = 13.8753675533549

x37 = -96.0803753222878

x38 = -17.540558982543

x39 = -74.0892267471593

x40 = -10.7337748997651

x41 = -1.83259571459405

x42 = 67.8060414399797

x43 = 61.5228561328001

x44 = -20.1585528605345

x45 = 35.8665161284835

x46 = 32.7249234748937

x47 = -30.1069295969022

x48 = -26.9653369433124

x49 = 55.2396708256205

x50 = -92.9387826686981

x51 = 76.7072206251508

x52 = 64.1408500107916

x53 = 74.0892267471593

x54 = -86.1319985859202

x55 = 77.2308194007491

x56 = -228.027266773059

x57 = 11.2573736753634

x58 = 39.5317075576716

x59 = -48.9564855184409

x60 = 99.2219679758776

x61 = -70.4240353179712

x62 = -42.1497014356631

x63 = 70.4240353179712

x64 = 96.0803753222878

x65 = -55.2396708256205

x66 = 30.1069295969022

x67 = 98.6983692002793

x68 = -77.2308194007491

x69 = -57.857664703612

x70 = -58.3812634792103

x71 = -64.1408500107916

x72 = -54.7160720500222

x73 = -48.4328867428426

x74 = 20.1585528605345

x75 = -89.7971900151083

x76 = -99.2219679758776

x77 = -8.11578102177363

x78 = 39.0081087820733

x79 = 17.540558982543

x80 = -45.8148928648512

x81 = 1336.48587471466

x82 = 33.248522250492

x83 = -89.27359123951

x84 = -61.5228561328001

x85 = -92.4151838930998

x86 = -67.8060414399797

x87 = -4.97418836818384

x88 = -35.8665161284835

x89 = -79.8488132787406

x90 = -13.8753675533549

x91 = 83.5140047079287

x92 = -98.6983692002793

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