sinx+4cosx=0 (уравнение)

Найду корень уравнения: sinx+4cosx=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)

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

=

-atan(4)

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

произведение

1*-atan(4)

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

=

-atan(4)

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

Численный ответ

x1 = 86.6387766368462

x2 = 42.6564794865891

x3 = 33.2317015258197

x4 = -89.2904119641822

x5 = 30.0901088722299

x6 = -98.7151899249516

x7 = 36.3732941794095

x8 = 70.9308133688972

x9 = -26.4585588923864

x10 = -54.7328927746945

x11 = 58.364442754538

x12 = 4.95736764351155

x13 = -17.033780931617

x14 = 39.5148868329993

x15 = 55.2228501009482

x16 = 67.7892207153074

x17 = 45.7980721401789

x18 = -48.4497074675149

x19 = 77.2139986760768

x20 = 61.5060354081278

x21 = 92.9219619440258

x22 = 52.0812574473585

x23 = -20.1753735852068

x24 = -111.281560539311

x25 = -7380.92696094609

x26 = 23.8069235650503

x27 = -67.2992633890537

x28 = -35.8833368531558

x29 = 80.3555913296666

x30 = -42.1665221603353

x31 = -79.8656340034129

x32 = -1.32581766366803

x33 = -7.60900297084762

x34 = 14.3821456042809

x35 = -86.1488193105924

x36 = 11.2405529506911

x37 = -95.5735972713618

x38 = -23.3169662387966

x39 = -64.1576707354639

x40 = 17.5237382578707

x41 = -13.8921882780272

x42 = -51.5913001211047

x43 = -92.432004617772

x44 = -70.4408560426435

x45 = 96.0635545976156

x46 = 8.09896029710135

x47 = -29.6001515459762

x48 = -57.8744854282843

x49 = 99.2051472512053

x50 = 26.9485162186401

x51 = 64.6476280617176

x52 = -10.7505956244374

x53 = 74.072406022487

x54 = 83.4971839832564

x55 = -39.0249295067456

x56 = -61.0160780818741

x57 = 1.81577498992176

x58 = -76.7240413498231

x59 = -45.3081148139251

x60 = -32.741744199566

x61 = 48.9396647937687

x62 = 20.6653309114605

x63 = -73.5824486962333

x64 = 89.780369290436

x65 = -4.46741031725783

x66 = -83.0072266570027

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