tg(-4x)=1/3 (уравнение)

Найду корень уравнения: tg(-4x)=1/3

Вы ввели

tan(-4*x) = 1/3

$$\tan{\left(- 4 x \right)} = \frac{1}{3}$$

Подробное решение

Дано уравнение
$$\tan{\left(- 4 x \right)} = \frac{1}{3}$$
- это простейшее тригонометрическое ур-ние

Разделим обе части ур-ния на -1

Ур-ние превратится в
$$\tan{\left(4 x \right)} = - \frac{1}{3}$$
Это ур-ние преобразуется в
$$4 x = \pi n + \operatorname{atan}{\left(- \frac{1}{3} \right)}$$
Или
$$4 x = \pi n - \operatorname{atan}{\left(\frac{1}{3} \right)}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$4$$
получим ответ:
$$x_{1} = \frac{\pi n}{4} - \frac{\operatorname{atan}{\left(\frac{1}{3} \right)}}{4}$$

Быстрый ответ

     -atan(1/3) 
x1 = -----------
          4     

$$x_{1} = - \frac{\operatorname{atan}{\left(\frac{1}{3} \right)}}{4}$$

Сумма и произведение корней

сумма

-atan(1/3) 
-----------
     4     

$$- \frac{\operatorname{atan}{\left(\frac{1}{3} \right)}}{4}$$

=

-atan(1/3) 
-----------
     4     

$$- \frac{\operatorname{atan}{\left(\frac{1}{3} \right)}}{4}$$

произведение

-atan(1/3) 
-----------
     4     

$$- \frac{\operatorname{atan}{\left(\frac{1}{3} \right)}}{4}$$

=

-atan(1/3) 
-----------
     4     

$$- \frac{\operatorname{atan}{\left(\frac{1}{3} \right)}}{4}$$

Численный ответ

x1 = -99.8260043900751

x2 = 95.7381382958895

x3 = 10.1297384855677

x4 = 21.9107109365294

x5 = -69.9808741809721

x6 = -55.843707239818

x7 = 61.9660172697993

x8 = -91.9720227561006

x9 = 39.9748686946707

x10 = -25.998577030715

x11 = -77.8348558149465

x12 = -59.7706980568052

x13 = -23.6423825405226

x14 = -15.7884009065481

x15 = -33.8525586646894

x16 = 11.7005348123626

x17 = 87.8841566619151

x18 = 94.1673419690946

x19 = 86.3133603351202

x20 = -62.1268925469976

x21 = -95.8990135730879

x22 = -18.1445953967405

x23 = -88.0450319391134

x24 = 100.450527276274

x25 = -54.2729109130231

x26 = 46.2580540018503

x27 = 24.2669054267217

x28 = -89.6158282659083

x29 = 17.9837201195422

x30 = -22.0715862137277

x31 = -36.2087531548818

x32 = 82.3863695181329

x33 = 78.4593787011457

x34 = -93.5428190828955

x35 = -85.688837448921

x36 = -58.1999017300103

x37 = 65.8930080867865

x38 = 33.6916833874911

x39 = -84.1180411221261

x40 = -98.2552080632802

x41 = -41.7065402986639

x42 = -71.551670507767

x43 = -37.7795494816767

x44 = 43.9018595116579

x45 = 58.039026452812

x46 = -5.5782247823813

x47 = 80.0301750279406

x48 = -0.0804376385991605

x49 = 72.1761933939661

x50 = 32.1208870606962

x51 = -27.5693733575098

x52 = -1.65123396539406

x53 = 64.3222117599916

x54 = 14.0567293025549

x55 = 83.9571658449278

x56 = -47.9897256058435

x57 = -7.93441927257364

x58 = 69.8199989037737

x59 = 3.84655317838808

x60 = -80.1910503051389

x61 = -32.2817623378945

x62 = 7.77354399537532

x63 = 36.0478778776835

x64 = -51.9167164228307

x65 = -10.290613762766

x66 = 90.2403511521074

x67 = -66.0538833639848

x68 = 38.4040723678758

x69 = -45.6335311156512

x70 = 42.331063184863

x71 = -67.6246796907797

x72 = 28.193896243709

x73 = 56.4682301260171

x74 = 98.0943327860819

x75 = 51.7558411456324

x76 = 68.2492025769788

x77 = 16.4129237927473

x78 = 50.1850448188375

x79 = 73.746989720761

x80 = 6.20274766858043

x81 = 2.27575685159318

x82 = -4.0074284555864

x83 = 29.7646925705039

x84 = -73.9078649979593

x85 = -76.2640594881516

x86 = 47.8288503286452

x87 = -44.0627347888563

x88 = -11.8614100895609

x89 = 60.3952209430044

x90 = -29.9255678477022

x91 = 20.3399146097345

x92 = -81.7618466319338

x93 = -49.5605219326384

x94 = 76.1031842109533

x95 = 54.1120356358248

x96 = 91.8111474789023

x97 = -40.135743971869

x98 = -63.6976888737925

x99 = -14.2176045797532

x100 = -19.7153917235354

x101 = 25.8377017535166

График