cos2x=√3/2 (уравнение)

Найду корень уравнения: cos2x=√3/2

Вы ввели

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

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

Подробное решение

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

Быстрый ответ

     pi
x1 = --
     12

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

     11*pi
x2 = -----
       12 

$$x_{2} = \frac{11 \pi}{12}$$

Сумма и произведение корней

сумма

    pi   11*pi
0 + -- + -----
    12     12 

$$\left(0 + \frac{\pi}{12}\right) + \frac{11 \pi}{12}$$

=

pi

$$\pi$$

произведение

  pi 11*pi
1*--*-----
  12   12 

$$\frac{11 \pi}{12} \cdot 1 \frac{\pi}{12}$$

=

     2
11*pi 
------
 144  

$$\frac{11 \pi^{2}}{144}$$

Численный ответ

x1 = 6.02138591938044

x2 = -87.7027949127151

x3 = 25.3945406165175

x4 = 24.8709418409192

x5 = -69.3768377667746

x6 = -43.720497762458

x7 = 100.269165527074

x8 = -100.269165527074

x9 = 66.2352451131848

x10 = 22.2529479629277

x11 = 18.5877565337396

x12 = 46.8620904160477

x13 = -232.739655753444

x14 = -37.9609112308767

x15 = 69.3768377667746

x16 = 0.261799387799149

x17 = -28.012534494509

x18 = 44.2440965380563

x19 = -47.3856891916461

x20 = -91.3679863419031

x21 = 78.2780169519457

x22 = -85.0848010347236

x23 = 31.6777259236971

x24 = 91.3679863419031

x25 = -3.40339204138894

x26 = 28.012534494509

x27 = -19.1113553093379

x28 = -31.6777259236971

x29 = -97.6511716490827

x30 = 47.3856891916461

x31 = 56.2868683768171

x32 = 12.30457122656

x33 = -12.30457122656

x34 = -40.5789051088682

x35 = 132.20869083857

x36 = 88.2263936883134

x37 = -63.093652459595

x38 = 62.5700536839967

x39 = 81.9432083811338

x40 = 90.8443875663049

x41 = 3.40339204138894

x42 = -56.2868683768171

x43 = -41.1025038844665

x44 = -71.9948316447661

x45 = 93.9859802198946

x46 = -9.68657734856853

x47 = -62.5700536839967

x48 = -15.9697626557481

x49 = 138.49187614575

x50 = 59.9520598060052

x51 = -93.9859802198946

x52 = -34.2957198016886

x53 = -25.3945406165175

x54 = -78.2780169519457

x55 = 75.6600230739542

x56 = -50.0036830696375

x57 = 71.9948316447661

x58 = -53.6688744988256

x59 = 97.6511716490827

x60 = 2.87979326579064

x61 = 40.5789051088682

x62 = -663.137849295245

x63 = -18.5877565337396

x64 = -75.6600230739542

x65 = 15.9697626557481

x66 = -103.934356956262

x67 = -59.9520598060052

x68 = 50.0036830696375

x69 = 37.9609112308767

x70 = -65.7116463375865

x71 = 34.2957198016886

x72 = -84.5612022591253

x73 = 9.68657734856853

x74 = 68.8532389911763

x75 = 53.6688744988256

x76 = -21.7293491873294

x77 = 84.5612022591253

x78 = -81.9432083811338

x79 = -6.02138591938044

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