cos(6x)=-sqrt(3)/2 (уравнение)

Найду корень уравнения: cos(6x)=-sqrt(3)/2

Вы ввели

              ___ 
           -\/ 3  
cos(6*x) = -------
              2   

$$\cos{\left(6 x \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$

Подробное решение

Дано уравнение
$$\cos{\left(6 x \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$6 x = \pi n + \operatorname{acos}{\left(- \frac{\sqrt{3}}{2} \right)}$$
$$6 x = \pi n - \pi + \operatorname{acos}{\left(- \frac{\sqrt{3}}{2} \right)}$$
Или
$$6 x = \pi n + \frac{5 \pi}{6}$$
$$6 x = \pi n - \frac{\pi}{6}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$6$$
получим ответ:
$$x_{1} = \frac{\pi n}{6} + \frac{5 \pi}{36}$$
$$x_{2} = \frac{\pi n}{6} - \frac{\pi}{36}$$

Быстрый ответ

     5*pi
x1 = ----
      36 

$$x_{1} = \frac{5 \pi}{36}$$

     7*pi
x2 = ----
      36 

$$x_{2} = \frac{7 \pi}{36}$$

Сумма и произведение корней

сумма

    5*pi   7*pi
0 + ---- + ----
     36     36 

$$\left(0 + \frac{5 \pi}{36}\right) + \frac{7 \pi}{36}$$

=

pi
--
3 

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

произведение

  5*pi 7*pi
1*----*----
   36   36 

$$\frac{7 \pi}{36} \cdot 1 \cdot \frac{5 \pi}{36}$$

=

     2
35*pi 
------
 1296 

$$\frac{35 \pi^{2}}{1296}$$

Численный ответ

x1 = -49.8291501444381

x2 = -36.0410490536829

x3 = 34.1211868764891

x4 = 12.1300383013606

x5 = -43.3714319120591

x6 = 29.9323966717028

x7 = 40.2298392584693

x8 = -55.9378025264183

x9 = -58.0321976288115

x10 = -99.9200996766754

x11 = 10.0356431989674

x12 = -23.6492113645232

x13 = -80.02334620394

x14 = 82.2922742315326

x15 = 49.8291501444381

x16 = 66.4097780383842

x17 = -55.0651379004211

x18 = -93.8114472946952

x19 = -77.9289511015468

x20 = 73.9146938219599

x21 = 86.3065315111196

x22 = 76.0090889243531

x23 = -87.3537290623162

x24 = 63.4427183099939

x25 = -51.7490123216319

x26 = -7.76671517137477

x27 = 22.4274808881271

x28 = -16.1442955809475

x29 = 90.495321715906

x30 = 5.846852994181

x31 = -21.55481626213

x32 = 93.8114472946952

x33 = -25.7436064669164

x34 = -98.0002374994816

x35 = 32.0267917740959

x36 = 92.5897168182992

x37 = 84.2121364087264

x38 = -54.0179403492245

x39 = 18.2386906833407

x40 = -33.9466539512897

x41 = 100.094632601875

x42 = 95.9058423970884

x43 = -3.75245789178781

x44 = -82.1177413063332

x45 = -60.1265927312047

x46 = -76.0090889243531

x47 = 56.1123354516177

x48 = -18.4132236085402

x49 = -67.6315085147803

x50 = 0.436332312998582

x51 = -40.4043721836687

x52 = 3.75245789178781

x53 = -27.8380015693096

x54 = -29.7578637465033

x55 = 14.2244334037538

x56 = -11.9555053761612

x57 = 7.9412480965742

x58 = -45.6403599396517

x59 = 51.9235452468313

x60 = -73.7401608967604

x61 = 62.2209878335978

x62 = 64.315382935991

x63 = 98.0002374994816

x64 = -880.25680824334

x65 = -9.86111027376796

x66 = -1.65806278939461

x67 = -95.731309471889

x68 = -69.7259036171735

x69 = 11.9555053761612

x70 = 60.3011256564041

x71 = -65.3625804871876

x72 = 54.0179403492245

x73 = -62.3955207587973

x74 = 88.4009266135128

x75 = -5.846852994181

x76 = -84.3866693339258

x77 = 28.8851991205062

x78 = 42.3242343608625

x79 = -14.0499004785544

x80 = 44.4186294632557

x81 = -47.7347550420449

x82 = 38.3099770812755

x83 = -71.8202987195667

x84 = 78.1034840267462

x85 = -89.6226570899088

x86 = 75.8345559991536

x87 = 20.3330857857339

x88 = -91.717052192302

x89 = 71.8202987195667

x90 = -38.1354441560761

x91 = 27.8380015693096

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