ctgx=1/4 (уравнение)

Найду корень уравнения: ctgx=1/4

Вы ввели

cot(x) = 1/4

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

Подробное решение

Дано уравнение
$$\cot{\left(x \right)} = \frac{1}{4}$$
преобразуем
$$\cot{\left(x \right)} - \frac{1}{4} = 0$$
$$\cot{\left(x \right)} - \frac{1}{4} = 0$$
Сделаем замену
$$w = \cot{\left(x \right)}$$
Переносим свободные слагаемые (без w)
из левой части в правую, получим:
$$w = \frac{1}{4}$$
Получим ответ: w = 1/4
делаем обратную замену
$$\cot{\left(x \right)} = w$$
подставляем w:

Быстрый ответ

x1 = acot(1/4)

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

Сумма и произведение корней

сумма

0 + acot(1/4)

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

=

acot(1/4)

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

произведение

1*acot(1/4)

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

=

acot(1/4)

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

Численный ответ

x1 = -17.5237382578707

x2 = 54.7328927746945

x3 = 57.8744854282843

x4 = 13.8921882780272

x5 = 70.4408560426435

x6 = -8.09896029710135

x7 = -92.9219619440258

x8 = -83.4971839832564

x9 = -39.5148868329993

x10 = 89.2904119641822

x11 = -33.2317015258197

x12 = -48.9396647937687

x13 = -80.3555913296666

x14 = 83.0072266570027

x15 = 7.60900297084762

x16 = 10.7505956244374

x17 = 29.6001515459762

x18 = -77.2139986760768

x19 = 17.033780931617

x20 = 98.7151899249516

x21 = 35.8833368531558

x22 = 39.0249295067456

x23 = 92.432004617772

x24 = -26.9485162186401

x25 = -42.6564794865891

x26 = -86.6387766368462

x27 = 64.1576707354639

x28 = -64.6476280617176

x29 = 32.741744199566

x30 = -61.5060354081278

x31 = -1.81577498992176

x32 = -67.7892207153074

x33 = 1.32581766366803

x34 = 67.2992633890537

x35 = -36.3732941794095

x36 = 73.5824486962333

x37 = 45.3081148139251

x38 = -11.2405529506911

x39 = 86.1488193105924

x40 = -4.95736764351155

x41 = 23.3169662387966

x42 = -23.8069235650503

x43 = -99.2051472512053

x44 = -14.3821456042809

x45 = 48.4497074675149

x46 = 79.8656340034129

x47 = 4.46741031725783

x48 = -70.9308133688972

x49 = 20.1753735852068

x50 = -55.2228501009482

x51 = 26.4585588923864

x52 = -30.0901088722299

x53 = 95.5735972713618

x54 = 42.1665221603353

x55 = 61.0160780818741

x56 = -89.780369290436

x57 = 76.7240413498231

x58 = -58.364442754538

x59 = 51.5913001211047

x60 = -96.0635545976156

x61 = -45.7980721401789

x62 = -52.0812574473585

x63 = -74.072406022487

x64 = -20.6653309114605

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