sin(x)-4cos(x)=0 (уравнение)

Найду корень уравнения: sin(x)-4cos(x)=0

Вы ввели

sin(x) - 4*cos(x) = 0

$$\sin{\left(x \right)} - 4 \cos{\left(x \right)} = 0$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} - 4 \cos{\left(x \right)} = 0$$
преобразуем:
$$\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} = 4$$
или
$$\tan{\left(x \right)} = 4$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{atan}{\left(-4 \right)}$$
Или
$$x = \pi n - \operatorname{atan}{\left(4 \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = atan(4)

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

Сумма и произведение корней

сумма

0 + atan(4)

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

=

atan(4)

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

произведение

1*atan(4)

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

=

atan(4)

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

Численный ответ

x1 = -102.346739904795

x2 = -17.5237382578707

x3 = 54.7328927746945

x4 = 57.8744854282843

x5 = 13.8921882780272

x6 = 70.4408560426435

x7 = -8.09896029710135

x8 = -92.9219619440258

x9 = -83.4971839832564

x10 = -39.5148868329993

x11 = 89.2904119641822

x12 = -33.2317015258197

x13 = -48.9396647937687

x14 = 101.856782578541

x15 = 83.0072266570027

x16 = -80.3555913296666

x17 = 7.60900297084762

x18 = 10.7505956244374

x19 = 29.6001515459762

x20 = -77.2139986760768

x21 = 17.033780931617

x22 = 98.7151899249516

x23 = 35.8833368531558

x24 = 39.0249295067456

x25 = 92.432004617772

x26 = -26.9485162186401

x27 = -42.6564794865891

x28 = -86.6387766368462

x29 = 64.1576707354639

x30 = -64.6476280617176

x31 = 32.741744199566

x32 = -265.709557891464

x33 = -61.5060354081278

x34 = -1.81577498992176

x35 = -67.7892207153074

x36 = 1.32581766366803

x37 = 67.2992633890537

x38 = -36.3732941794095

x39 = 73.5824486962333

x40 = 45.3081148139251

x41 = -11.2405529506911

x42 = 86.1488193105924

x43 = -4.95736764351155

x44 = 23.3169662387966

x45 = -23.8069235650503

x46 = -99.2051472512053

x47 = -14.3821456042809

x48 = 48.4497074675149

x49 = 79.8656340034129

x50 = 4.46741031725783

x51 = -70.9308133688972

x52 = 20.1753735852068

x53 = -55.2228501009482

x54 = 26.4585588923864

x55 = -30.0901088722299

x56 = 95.5735972713618

x57 = 42.1665221603353

x58 = 61.0160780818741

x59 = -89.780369290436

x60 = 76.7240413498231

x61 = -58.364442754538

x62 = 51.5913001211047

x63 = -96.0635545976156

x64 = -45.7980721401789

x65 = -52.0812574473585

x66 = -74.072406022487

x67 = -20.6653309114605

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