tan(x)=1/4 (уравнение)

Найду корень уравнения: tan(x)=1/4

Вы ввели

tan(x) = 1/4

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

Подробное решение

Дано уравнение
$$\tan{\left(x \right)} = \frac{1}{4}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{atan}{\left(\frac{1}{4} \right)}$$
Или
$$x = \pi n + \operatorname{atan}{\left(\frac{1}{4} \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = atan(1/4)

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

Сумма и произведение корней

сумма

0 + atan(1/4)

$$0 + \operatorname{atan}{\left(\frac{1}{4} \right)}$$

=

atan(1/4)

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

произведение

1*atan(1/4)

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

=

atan(1/4)

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

Численный ответ

x1 = -9.17979929764252

x2 = -90.8612082909771

x3 = -40.5957258335404

x4 = 53.6520537741534

x5 = 78.7847950028717

x6 = -34.3125405263609

x7 = -87.7196156373873

x8 = 97.6343509244105

x9 = -43.7373184871302

x10 = -15.4629846048221

x11 = 91.3511656172309

x12 = -94.0028009445669

x13 = -78.294837676618

x14 = -46.87891114072

x15 = 12.811349277486

x16 = 31.6609051990248

x17 = -37.4541331799507

x18 = 25.3777198918452

x19 = -97.1443935981567

x20 = -31.1709478727711

x21 = -100.285986251747

x22 = -21.7461699120017

x23 = 47.3688684669738

x24 = -84.5780229837976

x25 = 3.38657131671666

x26 = 66.2184243885125

x27 = -72.0116523694384

x28 = 100.775943578

x29 = 6.52816397030645

x30 = 19.0945345846656

x31 = 22.2361272382554

x32 = 34.8024978526146

x33 = -59.4452817550792

x34 = -62.586874408669

x35 = -2.89661399046293

x36 = -24.8877625655915

x37 = 88.2095729636411

x38 = 81.9263876564615

x39 = 37.9440905062044

x40 = -56.3036891014894

x41 = -65.7284670622588

x42 = 72.5016096956921

x43 = -12.3213919512323

x44 = 50.5104611205636

x45 = -28.0293552191813

x46 = -18.6045772584119

x47 = -6.03820664405272

x48 = 44.227275813384

x49 = -75.1532450230282

x50 = -53.1620964478996

x51 = 56.7936464277431

x52 = 75.6432023492819

x53 = -68.8700597158486

x54 = 59.9352390813329

x55 = -50.0205037943098

x56 = 63.0768317349227

x57 = -81.4364303302078

x58 = 9.66975662389624

x59 = 69.3600170421023

x60 = 41.0856831597942

x61 = 28.519312545435

x62 = 0.244978663126864

x63 = 85.0679803100513

x64 = 15.9529419310758

x65 = 94.4927582708207

График