tan(x)=17/20 (уравнение)

Найду корень уравнения: tan(x)=17/20

Вы ввели

         17
tan(x) = --
         20

$$\tan{\left(x \right)} = \frac{17}{20}$$

Подробное решение

Дано уравнение
$$\tan{\left(x \right)} = \frac{17}{20}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{atan}{\left(\frac{17}{20} \right)}$$
Или
$$x = \pi n + \operatorname{atan}{\left(\frac{17}{20} \right)}$$
, где n - любое целое число

Быстрый ответ

         /17\
x1 = atan|--|
         \20/

$$x_{1} = \operatorname{atan}{\left(\frac{17}{20} \right)}$$

Сумма и произведение корней

сумма

        /17\
0 + atan|--|
        \20/

$$0 + \operatorname{atan}{\left(\frac{17}{20} \right)}$$

=

    /17\
atan|--|
    \20/

$$\operatorname{atan}{\left(\frac{17}{20} \right)}$$

произведение

      /17\
1*atan|--|
      \20/

$$1 \operatorname{atan}{\left(\frac{17}{20} \right)}$$

=

    /17\
atan|--|
    \20/

$$\operatorname{atan}{\left(\frac{17}{20} \right)}$$

Численный ответ

x1 = 10.1292720250116

x2 = -74.6937296219128

x3 = 54.1115691752687

x4 = 35.2620132537299

x5 = -21.2866545108863

x6 = 91.8106810183462

x7 = -77.8353222755026

x8 = 25.8372352929606

x9 = 57.2531618288585

x10 = 79.244310403987

x11 = 44.6867912144993

x12 = 101.235458979116

x13 = -43.2778030860149

x14 = 98.0938663255258

x15 = -15.0034692037067

x16 = -36.9946177788353

x17 = 69.8195324432177

x18 = -8.72028389652716

x19 = -33.8530251252455

x20 = 63.5363471360381

x21 = -71.552136968323

x22 = -80.9769149290924

x23 = -84.1185075826822

x24 = -46.4193957396047

x25 = -11.861876550117

x26 = 60.3947544824483

x27 = 3.84608671783201

x28 = 41.5451985609095

x29 = -93.5432855434516

x30 = -68.4105443147332

x31 = 76.1027177503973

x32 = 19.554049985781

x33 = -24.4282471644761

x34 = -27.5698398180659

x35 = -96.6848781970414

x36 = -65.2689516611434

x37 = -2.43709858934758

x38 = -40.1362104324251

x39 = 22.6956426393708

x40 = 32.1204206001402

x41 = 85.5274957111666

x42 = 94.952273671936

x43 = -5.57869124293737

x44 = -62.1273590075537

x45 = 6.9876793714218

x46 = 50.9699765216789

x47 = -52.7025810467843

x48 = 88.6690883647564

x49 = -58.9857663539639

x50 = -49.5609883931945

x51 = 28.9788279465504

x52 = 72.9611250968075

x53 = 47.8283838680891

x54 = -90.4016928898618

x55 = -87.260100236272

x56 = -30.7114324716557

x57 = 38.4036059073197

x58 = 82.3859030575768

x59 = 0.704494064242218

x60 = -55.8441737003741

x61 = -99.8264708506312

x62 = 66.6779397896279

x63 = 13.2708646786014

x64 = -18.1450618572965

x65 = 16.4124573321912

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