cos3x=-1/2 (уравнение)

Найду корень уравнения: cos3x=-1/2

Вы ввели

cos(3*x) = -1/2

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

Подробное решение

Дано уравнение
$$\cos{\left(3 x \right)} = - \frac{1}{2}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$3 x = \pi n + \operatorname{acos}{\left(- \frac{1}{2} \right)}$$
$$3 x = \pi n - \pi + \operatorname{acos}{\left(- \frac{1}{2} \right)}$$
Или
$$3 x = \pi n + \frac{2 \pi}{3}$$
$$3 x = \pi n - \frac{\pi}{3}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$3$$
получим ответ:
$$x_{1} = \frac{\pi n}{3} + \frac{2 \pi}{9}$$
$$x_{2} = \frac{\pi n}{3} - \frac{\pi}{9}$$

Быстрый ответ

     2*pi
x1 = ----
      9  

$$x_{1} = \frac{2 \pi}{9}$$

     4*pi
x2 = ----
      9  

$$x_{2} = \frac{4 \pi}{9}$$

Сумма и произведение корней

сумма

2*pi   4*pi
---- + ----
 9      9  

$$\frac{2 \pi}{9} + \frac{4 \pi}{9}$$

=

2*pi
----
 3  

$$\frac{2 \pi}{3}$$

произведение

2*pi 4*pi
----*----
 9    9  

$$\frac{2 \pi}{9} \frac{4 \pi}{9}$$

=

    2
8*pi 
-----
  81 

$$\frac{8 \pi^{2}}{81}$$

Численный ответ

x1 = -18.151424220741

x2 = -45.3785605518526

x3 = -30.0196631343025

x4 = 16.0570291183478

x5 = -62.1337213709981

x6 = 4.88692190558412

x7 = 78.190750489346

x8 = -82.3795406941324

x9 = 22.3402144255274

x10 = 1.39626340159546

x11 = 49.567350756639

x12 = 84.4739357965256

x13 = 25.8308729295161

x14 = -23.7364778271229

x15 = 97.7384381116825

x16 = 30.0196631343025

x17 = -71.9075651821664

x18 = -67.71877497738

x19 = -13.9626340159546

x20 = 6.98131700797732

x21 = -27.9252680319093

x22 = -97.7384381116825

x23 = 86.5683308989187

x24 = 34.2084533390889

x25 = -3.49065850398866

x26 = -32.1140582366957

x27 = 69.8131700797732

x28 = 7.67944870877505

x29 = -93.5496479068961

x30 = 76.0963553869528

x31 = -74.0019602845596

x32 = -5.58505360638185

x33 = -95.6440430092893

x34 = 87.2664625997165

x35 = -99.8328332140756

x36 = 38.3972435438752

x37 = -36.3028484414821

x38 = -16.0570291183478

x39 = 74.0019602845596

x40 = 68.4169066781777

x41 = 55.8505360638185

x42 = 71.9075651821664

x43 = 24.4346095279206

x44 = -11.8682389135614

x45 = 62.1337213709981

x46 = 20.2458193231342

x47 = -49.567350756639

x48 = 95.6440430092893

x49 = 27.9252680319093

x50 = -7.67944870877505

x51 = 40.4916386462684

x52 = -9.77384381116824

x53 = 48.8692190558412

x54 = -21.6420827247297

x55 = 44.6804288510548

x56 = 66.3225115757845

x57 = -69.8131700797732

x58 = -47.4729556542458

x59 = -60.0393262686049

x60 = -55.8505360638185

x61 = -80.2851455917392

x62 = 92.8515162060983

x63 = -41.1897703470662

x64 = -51.6617458590322

x65 = 80.2851455917392

x66 = -78.190750489346

x67 = -57.9449311662117

x68 = 32.1140582366957

x69 = -65.6243798749868

x70 = 51.6617458590322

x71 = 82.3795406941324

x72 = -76.0963553869528

x73 = -34.2084533390889

x74 = -25.8308729295161

x75 = 42.5860337486616

x76 = -1.39626340159546

x77 = 99.8328332140756

x78 = -247.836753783195

x79 = -38.3972435438752

x80 = 9.77384381116824

x81 = -91.4552528045029

x82 = 45.3785605518526

x83 = 60.0393262686049

x84 = 57.9449311662117

x85 = 53.7561409614254

x86 = 36.3028484414821

x87 = -89.3608577021097

x88 = 11.8682389135614

x89 = 64.2281164733913

x90 = 88.6627260013119

x91 = 13.9626340159546

x92 = -53.7561409614254

x93 = 18.151424220741

График