cos(2*x-pi/3)=0 (уравнение)

Найду корень уравнения: cos(2*x-pi/3)=0

Вы ввели

   /      pi\    
cos|2*x - --| = 0
   \      3 /    

$$\cos{\left(2 x - \frac{\pi}{3} \right)} = 0$$

Подробное решение

Дано уравнение
$$\cos{\left(2 x - \frac{\pi}{3} \right)} = 0$$
- это простейшее тригонометрическое ур-ние

с изменением знака при 0

Получим:
$$\cos{\left(2 x - \frac{\pi}{3} \right)} = 0$$
Это ур-ние преобразуется в
$$2 x + \frac{\pi}{6} = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$2 x + \frac{\pi}{6} = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
Или
$$2 x + \frac{\pi}{6} = 2 \pi n$$
$$2 x + \frac{\pi}{6} = 2 \pi n + \pi$$
, где n - любое целое число
Перенесём
$$\frac{\pi}{6}$$
в правую часть ур-ния
с противоположным знаком, итого:
$$2 x = 2 \pi n - \frac{\pi}{6}$$
$$2 x = 2 \pi n + \frac{5 \pi}{6}$$
Разделим обе части полученного ур-ния на
$$2$$
получим ответ:
$$x_{1} = \pi n - \frac{\pi}{12}$$
$$x_{2} = \pi n + \frac{5 \pi}{12}$$

Сумма и произведение корней

сумма

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

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

=

pi
--
3 

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

произведение

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

$$\frac{5 \pi}{12} \cdot 1 \left(- \frac{\pi}{12}\right)$$

=

     2
-5*pi 
------
 144  

$$- \frac{5 \pi^{2}}{144}$$

Быстрый ответ

     -pi 
x1 = ----
      12 

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

     5*pi
x2 = ----
      12 

$$x_{2} = \frac{5 \pi}{12}$$

Численный ответ

x1 = 6.02138591938044

x2 = -69.3768377667746

x3 = 35.8665161284835

x4 = 100.269165527074

x5 = -108.646745936647

x6 = -22.2529479629277

x7 = -96.0803753222878

x8 = 18.5877565337396

x9 = -37.9609112308767

x10 = -39.5317075576716

x11 = 21.7293491873294

x12 = 95.5567765466895

x13 = -94.5095789954929

x14 = -89.7971900151083

x15 = 32.7249234748937

x16 = 43.720497762458

x17 = -33.248522250492

x18 = 4.45058959258554

x19 = 103.410758180664

x20 = -58.3812634792103

x21 = 7.59218224617533

x22 = -45.8148928648512

x23 = -47.3856891916461

x24 = -91.3679863419031

x25 = 78.2780169519457

x26 = -72.5184304203644

x27 = -8.11578102177363

x28 = -15882.583459611

x29 = 54.7160720500222

x30 = -3.40339204138894

x31 = 26.4417381677141

x32 = 73.565627971561

x33 = 28.012534494509

x34 = -1.83259571459405

x35 = 70.4240353179712

x36 = -67.8060414399797

x37 = -66.2352451131848

x38 = -31.6777259236971

x39 = 64.1408500107916

x40 = -97.6511716490827

x41 = 56.2868683768171

x42 = 10.7337748997651

x43 = -11.2573736753634

x44 = -44.2440965380563

x45 = 48.4328867428426

x46 = 12.30457122656

x47 = 79.8488132787406

x48 = -14.3989663289532

x49 = 51.5744793964324

x50 = 62.5700536839967

x51 = -88.2263936883134

x52 = 86.1319985859202

x53 = 29.5833308213039

x54 = 92.4151838930998

x55 = 93.9859802198946

x56 = -83.5140047079287

x57 = 87.7027949127151

x58 = -9.68657734856853

x59 = 42.1497014356631

x60 = -15.9697626557481

x61 = -0.261799387799149

x62 = 65.7116463375865

x63 = -17.540558982543

x64 = 76.7072206251508

x65 = 98.6983692002793

x66 = -25.3945406165175

x67 = -61.5228561328001

x68 = 71.9948316447661

x69 = -53.6688744988256

x70 = -52.0980781720307

x71 = 40.5789051088682

x72 = -80.3724120543389

x73 = -75.6600230739542

x74 = 13.8753675533549

x75 = -77.2308194007491

x76 = -59.9520598060052

x77 = 50.0036830696375

x78 = -23.8237442897226

x79 = -55.2396708256205

x80 = -36.3901149040818

x81 = 34.2957198016886

x82 = 57.857664703612

x83 = -74.0892267471593

x84 = 635.910712964134

x85 = 84.5612022591253

x86 = -81.9432083811338

x87 = 20.1585528605345

x88 = -30.1069295969022

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