3cos(3x+2)= 0 (уравнение)

Найду корень уравнения: 3cos(3x+2)= 0

Вы ввели

3*cos(3*x + 2) = 0

$$3 \cos{\left(3 x + 2 \right)} = 0$$

Подробное решение

Дано уравнение
$$3 \cos{\left(3 x + 2 \right)} = 0$$
- это простейшее тригонометрическое ур-ние

с изменением знака при 0

Получим:
$$3 \cos{\left(3 x + 2 \right)} = 0$$

Разделим обе части ур-ния на 3

Ур-ние превратится в
$$\cos{\left(3 x + 2 \right)} = 0$$
Это ур-ние преобразуется в
$$3 x + 2 = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$3 x + 2 = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
Или
$$3 x + 2 = \pi n + \frac{\pi}{2}$$
$$3 x + 2 = \pi n - \frac{\pi}{2}$$
, где n - любое целое число
Перенесём
$$2$$
в правую часть ур-ния
с противоположным знаком, итого:
$$3 x = \pi n - 2 + \frac{\pi}{2}$$
$$3 x = \pi n - 2 - \frac{\pi}{2}$$
Разделим обе части полученного ур-ния на
$$3$$
получим ответ:
$$x_{1} = \frac{\pi n}{3} - \frac{2}{3} + \frac{\pi}{6}$$
$$x_{2} = \frac{\pi n}{3} - \frac{2}{3} - \frac{\pi}{6}$$

Быстрый ответ

       2   pi
x1 = - - + --
       3   6 

$$x_{1} = - \frac{2}{3} + \frac{\pi}{6}$$

       2   pi
x2 = - - + --
       3   2 

$$x_{2} = - \frac{2}{3} + \frac{\pi}{2}$$

Численный ответ

x1 = 70.0191680391037

x2 = -45.1725625925221

x3 = 36.5088464008126

x4 = -33.6533895293595

x5 = 21.8480806840602

x6 = -23.1814140173935

x7 = -44.1253650413255

x8 = 65.8303778343173

x9 = 58.4999949759411

x10 = -83.9188719867962

x11 = 41.7448341567955

x12 = -61.9277234116676

x13 = 87.8215264094458

x14 = -57.7389332068812

x15 = 43.8392292591887

x16 = -86.0132670891894

x17 = 50.1224145663683

x18 = -37.8421797341459

x19 = -5.37905564705136

x20 = -0.143067891068368

x21 = -17.9454262614105

x22 = 85.7271313070526

x23 = -75.5412915772234

x24 = 92.0103166142322

x25 = 72.1135631414969

x26 = -42.0309699389323

x27 = 26.0368708888466

x28 = -92.296452396369

x29 = 74.2079582438901

x30 = -70.3053038212404

x31 = -59.8333283092744

x32 = -2.23746299346156

x33 = -46.2197601437187

x34 = -7.47345074944455

x35 = 6.14011741611122

x36 = 12.4233027232908

x37 = -88.1076621915826

x38 = -79.7300817820098

x39 = 56.4055998735479

x40 = 1.95132721132483

x41 = -29.4645993245731

x42 = 17.6592904792738

x43 = -9.56784585183775

x44 = -11.6622409542309

x45 = -15.8510311590173

x46 = 59.5471925271377

x47 = -73.4468964748302

x48 = 94.1047117166254

x49 = 100.387897023805

x50 = -77.6356866796166

x51 = 78.3967484486765

x52 = -96.4852426011554

x53 = -68.2109087188472

x54 = 76.3023533462833

x55 = -39.9365748365391

x56 = 2.99852476252143

x57 = 8.23451251850442

x58 = -35.7477846317527

x59 = -64.0221185140608

x60 = 45.9336243615819

x61 = 52.2168096687615

x62 = 4.04572231371802

x63 = 10.3289076208976

x64 = -97.532440152352

x65 = 28.1312659912398

x66 = 81.5383411022663

x67 = -170.836268736114

x68 = -27.3702042221799

x69 = -55.644538104488

x70 = 23.9424757864534

x71 = -71.352501372437

x72 = -31.5589944269663

x73 = -51.4557478997017

x74 = 89.915921511839

x75 = 98.2935019214118

x76 = -20.0398213638037

x77 = -90.2020572939758

x78 = 80.4911435510697

x79 = -81.824476884403

x80 = 19.753685581667

x81 = -53.5501430020949

x82 = -24.2286115685901

x83 = -13.7566360566241

x84 = 48.0280194639751

x85 = 67.9247729367105

x86 = -99.6268352547452

x87 = 63.7359827319241

x88 = 96.1991068190186

x89 = 32.3200561960262

x90 = 14.517697825684

x91 = 54.3112047711547

x92 = 84.6799337558561

x93 = -22.1342164661969

x94 = 34.4144512984194

x95 = -66.116513616454

x96 = 30.225661093633

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