4+2cos6x=3 (уравнение)

Найду корень уравнения: 4+2cos6x=3

Вы ввели

4 + 2*cos(6*x) = 3

$$2 \cos{\left(6 x \right)} + 4 = 3$$

Подробное решение

Дано уравнение
$$2 \cos{\left(6 x \right)} + 4 = 3$$
- это простейшее тригонометрическое ур-ние

Разделим обе части ур-ния на 2

Ур-ние превратится в
$$\cos{\left(6 x \right)} = - \frac{1}{2}$$
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
-- + ----
9     9  

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

=

pi
--
3 

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

произведение

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

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

=

    2
2*pi 
-----
  81 

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

Численный ответ

x1 = 86.2192650485199

x2 = -18.151424220741

x3 = -35.9537825910832

x4 = 3.49065850398866

x5 = -30.0196631343025

x6 = 16.0570291183478

x7 = -62.1337213709981

x8 = 78.190750489346

x9 = 6.63225115757845

x10 = 22.3402144255274

x11 = -84.1248699461267

x12 = 82.0304748437335

x13 = 93.8987137572949

x14 = -23.7364778271229

x15 = 49.9164166070378

x16 = 90.7571211037051

x17 = 30.0196631343025

x18 = -71.9075651821664

x19 = -79.9360797413403

x20 = -67.71877497738

x21 = 54.1052068118242

x22 = -13.9626340159546

x23 = -27.9252680319093

x24 = -97.7384381116825

x25 = 34.2084533390889

x26 = -1.74532925199433

x27 = 76.0963553869528

x28 = 12.2173047639603

x29 = -74.0019602845596

x30 = -75.7472895365539

x31 = -99.8328332140756

x32 = -5.93411945678072

x33 = 25.4818070791172

x34 = -16.0570291183478

x35 = -52.010811709431

x36 = 74.0019602845596

x37 = -49.9164166070378

x38 = 71.9075651821664

x39 = -45.7276264022514

x40 = -87.6155284501153

x41 = -3.83972435438753

x42 = 83.0776723949301

x43 = -11.8682389135614

x44 = 62.1337213709981

x45 = 20.2458193231342

x46 = -77.8416846389471

x47 = 27.9252680319093

x48 = 95.9931088596881

x49 = -9.77384381116824

x50 = 10.1229096615671

x51 = -31.7649923862968

x52 = -91.8043186549017

x53 = -21.6420827247297

x54 = 90.4080552533063

x55 = 44.331363000656

x56 = 38.0481776934764

x57 = -82.0304748437335

x58 = 66.3225115757845

x59 = -8.02851455917392

x60 = -69.8131700797732

x61 = 98.0875039620813

x62 = -60.0393262686049

x63 = 5.93411945678072

x64 = -55.8505360638185

x65 = 80.2851455917392

x66 = -93.8987137572949

x67 = 45.7276264022514

x68 = -57.9449311662117

x69 = 32.1140582366957

x70 = -65.6243798749868

x71 = -43.6332312998582

x72 = 68.7659725285766

x73 = 88.3136601509131

x74 = -25.8308729295161

x75 = -47.8220215046446

x76 = 100.181899064475

x77 = -91.4552528045029

x78 = 60.0393262686049

x79 = -40.1425727958696

x80 = 56.1996019142174

x81 = 40.1425727958696

x82 = -33.85938748869

x83 = -95.9931088596881

x84 = 0.349065850398866

x85 = -89.7099235525085

x86 = 42.2369678982628

x87 = 8.02851455917392

x88 = 84.1248699461267

x89 = 64.2281164733913

x90 = 13.9626340159546

x91 = -38.0481776934764

x92 = -53.7561409614254

x93 = 18.151424220741

x94 = 34.9065850398866

x95 = 52.010811709431

График