2tg3x=1 (уравнение)

Найду корень уравнения: 2tg3x=1

Вы ввели

2*tan(3*x) = 1

$$2 \tan{\left(3 x \right)} = 1$$

Подробное решение

Дано уравнение
$$2 \tan{\left(3 x \right)} = 1$$
- это простейшее тригонометрическое ур-ние

Разделим обе части ур-ния на 2

Ур-ние превратится в
$$\tan{\left(3 x \right)} = \frac{1}{2}$$
Это ур-ние преобразуется в
$$3 x = \pi n + \operatorname{atan}{\left(\frac{1}{2} \right)}$$
Или
$$3 x = \pi n + \operatorname{atan}{\left(\frac{1}{2} \right)}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$3$$
получим ответ:
$$x_{1} = \frac{\pi n}{3} + \frac{\operatorname{atan}{\left(\frac{1}{2} \right)}}{3}$$

Быстрый ответ

     atan(1/2)
x1 = ---------
         3    

$$x_{1} = \frac{\operatorname{atan}{\left(\frac{1}{2} \right)}}{3}$$

Сумма и произведение корней

сумма

atan(1/2)
---------
    3    

$$\frac{\operatorname{atan}{\left(\frac{1}{2} \right)}}{3}$$

=

atan(1/2)
---------
    3    

$$\frac{\operatorname{atan}{\left(\frac{1}{2} \right)}}{3}$$

произведение

atan(1/2)
---------
    3    

$$\frac{\operatorname{atan}{\left(\frac{1}{2} \right)}}{3}$$

=

atan(1/2)
---------
    3    

$$\frac{\operatorname{atan}{\left(\frac{1}{2} \right)}}{3}$$

Численный ответ

x1 = 39.948056148471

x2 = 74.5055753379587

x3 = -79.4324646879412

x4 = -52.2053283568296

x5 = 2.24894430539346

x6 = -23.9309944745215

x7 = 54.6088218652234

x8 = -96.1876255070867

x9 = -28.1197846793079

x10 = 50.420031660437

x11 = -63.7245014199922

x12 = 15.8625124709492

x13 = -99.3292181606765

x14 = -30.2141797817011

x15 = 96.4967239130873

x16 = 36.8064634948812

x17 = 58.7976120700097

x18 = 81.8359581963349

x19 = -65.8188965223854

x20 = -72.102081829565

x21 = -19.7422042697351

x22 = -33.3557724352909

x23 = 98.5911190154805

x24 = 88.1191435035145

x25 = -11.3646238601623

x26 = -9.27022875776911

x27 = 90.2135386059077

x28 = -91.9988353023003

x29 = 10.6265247149662

x30 = 68.2223900307791

x31 = -17.6478091673419

x32 = 44.1368463532574

x33 = 80.7887606451383

x34 = -48.0165381520432

x35 = 48.3256365580438

x36 = 59.8448096212063

x37 = -43.8277479472568

x38 = 56.7032169676165

x39 = -1.93984589939293

x40 = -41.7333528448636

x41 = 28.4288830853084

x42 = -97.2348230582833

x43 = -83.6212548927275

x44 = -89.9044401999071

x45 = 86.0247484011213

x46 = 100.685514117874

x47 = -39.6389577424704

x48 = -70.0076867271718

x49 = 46.2312414556506

x50 = 34.712068392488

x51 = -87.8100450975139

x52 = 26.3344879829152

x53 = -61.630106317599

x54 = -21.8365993721283

x55 = 61.9392047235995

x56 = -37.5445626400773

x57 = -94.0932304046935

x58 = 92.3079337083009

x59 = 8.53212961257305

x60 = 72.4111802355655

x61 = 17.9569075733424

x62 = 78.6943655427451

x63 = -75.2436744831548

x64 = 42.0424512508642

x65 = 66.1279949283859

x66 = 4.34333940778666

x67 = -85.7156499951207

x68 = -55.3469210104194

x69 = 0.154549203000269

x70 = -57.4413161128126

x71 = -53.2525259080262

x72 = -67.9132916247786

x73 = 30.5232781877016

x74 = 37.8536610460778

x75 = -74.1964769319582

x76 = 14.8153149197526

x77 = -4.03424100178612

x78 = 94.4023288106941

x79 = 6.43773451017986

x80 = -26.0253895769147

x81 = -13.4590189625555

x82 = 32.6176732900948

x83 = 83.9303532987281

x84 = 24.240092880522

x85 = -81.5268597903344

x86 = -77.338069585548

x87 = -8.22303120657251

x88 = 22.1456977781288

x89 = -59.5357112152058

x90 = -6.12863610417932

x91 = 20.0513026757356

x92 = 12.7209198173594

x93 = -45.92214304965

x94 = 52.5144267628302

x95 = -50.1109332544364

x96 = -35.4501675376841

x97 = 70.3167851331723

x98 = 76.5999704403519

x99 = -15.5534140649487

x100 = 64.0335998259927

x101 = -31.2613773328977

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