cos6x=-1/2 (уравнение)

Найду корень уравнения: cos6x=-1/2

Вы ввели

cos(6*x) = -1/2

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

Подробное решение

Дано уравнение
$$\cos{\left(6 x \right)} = - \frac{1}{2}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$6 x = \pi n + \operatorname{acos}{\left(- \frac{1}{2} \right)}$$
$$6 x = \pi n - \pi + \operatorname{acos}{\left(- \frac{1}{2} \right)}$$
Или
$$6 x = \pi n + \frac{2 \pi}{3}$$
$$6 x = \pi n - \frac{\pi}{3}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$6$$
получим ответ:
$$x_{1} = \frac{\pi n}{6} + \frac{\pi}{9}$$
$$x_{2} = \frac{\pi n}{6} - \frac{\pi}{18}$$

Быстрый ответ

     pi
x1 = --
     9 

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

     2*pi
x2 = ----
      9  

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

Сумма и произведение корней

сумма

    pi   2*pi
0 + -- + ----
    9     9  

$$\left(0 + \frac{\pi}{9}\right) + \frac{2 \pi}{9}$$

=

pi
--
3 

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

произведение

  pi 2*pi
1*--*----
  9   9  

$$\frac{2 \pi}{9} \cdot 1 \frac{\pi}{9}$$

=

    2
2*pi 
-----
  81 

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

Численный ответ

x1 = -93.8987137572949

x2 = -99.8328332140756

x3 = 32.1140582366957

x4 = 34.2084533390889

x5 = -95.9931088596881

x6 = 52.010811709431

x7 = 78.190750489346

x8 = -16.0570291183478

x9 = -52.010811709431

x10 = 49.9164166070378

x11 = 22.3402144255274

x12 = -77.8416846389471

x13 = -9.77384381116824

x14 = -91.8043186549017

x15 = 12.2173047639603

x16 = -3.83972435438753

x17 = 84.1248699461267

x18 = 40.1425727958696

x19 = 30.0196631343025

x20 = 83.0776723949301

x21 = 80.2851455917392

x22 = 98.0875039620813

x23 = 34.9065850398866

x24 = 100.181899064475

x25 = 44.331363000656

x26 = 90.7571211037051

x27 = 42.2369678982628

x28 = -67.71877497738

x29 = -60.0393262686049

x30 = 54.1052068118242

x31 = -89.7099235525085

x32 = 71.9075651821664

x33 = 0.349065850398866

x34 = 10.1229096615671

x35 = -84.1248699461267

x36 = 60.0393262686049

x37 = -27.9252680319093

x38 = -11.8682389135614

x39 = -57.9449311662117

x40 = -45.7276264022514

x41 = -18.151424220741

x42 = -91.4552528045029

x43 = -35.9537825910832

x44 = 18.151424220741

x45 = -55.8505360638185

x46 = -87.6155284501153

x47 = 64.2281164733913

x48 = -30.0196631343025

x49 = 82.0304748437335

x50 = 74.0019602845596

x51 = -21.6420827247297

x52 = 93.8987137572949

x53 = -75.7472895365539

x54 = -79.9360797413403

x55 = -97.7384381116825

x56 = -38.0481776934764

x57 = 27.9252680319093

x58 = -43.6332312998582

x59 = 5.93411945678072

x60 = 88.3136601509131

x61 = 8.02851455917392

x62 = 56.1996019142174

x63 = -82.0304748437335

x64 = -31.7649923862968

x65 = -62.1337213709981

x66 = 6.63225115757845

x67 = -49.9164166070378

x68 = -5.93411945678072

x69 = 86.2192650485199

x70 = 66.3225115757845

x71 = -23.7364778271229

x72 = 13.9626340159546

x73 = -25.8308729295161

x74 = 68.7659725285766

x75 = 62.1337213709981

x76 = 3.49065850398866

x77 = -65.6243798749868

x78 = -71.9075651821664

x79 = 76.0963553869528

x80 = 20.2458193231342

x81 = 95.9931088596881

x82 = -33.85938748869

x83 = 90.4080552533063

x84 = -40.1425727958696

x85 = -74.0019602845596

x86 = -8.02851455917392

x87 = 38.0481776934764

x88 = 16.0570291183478

x89 = -53.7561409614254

x90 = -1.74532925199433

x91 = 25.4818070791172

x92 = -69.8131700797732

x93 = -13.9626340159546

x94 = -47.8220215046446

x95 = 45.7276264022514

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