sin(x)+5cos(x)=0 (уравнение)

Найду корень уравнения: sin(x)+5cos(x)=0

Вы ввели

sin(x) + 5*cos(x) = 0

$$\sin{\left(x \right)} + 5 \cos{\left(x \right)} = 0$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} + 5 \cos{\left(x \right)} = 0$$
преобразуем:
$$\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} = -5$$
или
$$\tan{\left(x \right)} = -5$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{atan}{\left(5 \right)}$$
Или
$$x = \pi n + \operatorname{atan}{\left(5 \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = -atan(5)

$$x_{1} = - \operatorname{atan}{\left(5 \right)}$$

Сумма и произведение корней

сумма

0 - atan(5)

$$- \operatorname{atan}{\left(5 \right)} + 0$$

=

-atan(5)

$$- \operatorname{atan}{\left(5 \right)}$$

произведение

1*-atan(5)

$$1 \left(- \operatorname{atan}{\left(5 \right)}\right)$$

=

-atan(5)

$$- \operatorname{atan}{\left(5 \right)}$$

Численный ответ

x1 = -89.3379950674592

x2 = -48.4972905707919

x3 = 64.6000449584406

x4 = 36.3257110761325

x5 = -13.9397713813042

x6 = 48.8920816904917

x7 = 26.9009331153631

x8 = -73.6300317995103

x9 = -57.9220685315613

x10 = -70.4884391459205

x11 = 45.7504890369019

x12 = -215.001701211051

x13 = 8.05137719382436

x14 = 67.7416376120304

x15 = -51.6388832243817

x16 = -67.3468464923307

x17 = 92.8743788407488

x18 = 20.6177478081835

x19 = -23.3645493420736

x20 = -17.081364034894

x21 = -95.6211803746388

x22 = -4.51499342053481

x23 = 80.3080082263896

x24 = -39.0725126100225

x25 = 1.76819188664478

x26 = 30.0425257689529

x27 = -76.7716244531001

x28 = -32.7893273028429

x29 = -92.479587721049

x30 = -64.2052538387409

x31 = 70.8832302656202

x32 = 74.02482291921

x33 = -45.3556979172021

x34 = -42.2141052636123

x35 = -20.2229566884838

x36 = -54.7804758779715

x37 = 96.0159714943386

x38 = 89.732786187159

x39 = 58.3168596512611

x40 = -61.0636611851511

x41 = 83.4496008799794

x42 = 99.1575641479284

x43 = 61.4584523048509

x44 = 23.7593404617733

x45 = -29.6477346492532

x46 = -79.9132171066898

x47 = -35.9309199564327

x48 = 77.1664155727998

x49 = -1.37340076694502

x50 = 17.4761551545937

x51 = -7.6565860741246

x52 = -83.0548097602796

x53 = 55.1752669976713

x54 = 39.4673037297223

x55 = 4.90978454023457

x56 = -98.7627730282286

x57 = 52.0336743440815

x58 = 11.1929698474142

x59 = 33.1841184225427

x60 = -86.1964024138694

x61 = -26.5061419956634

x62 = -10.7981787277144

x63 = 14.3345625010039

x64 = 42.6088963833121

x65 = 86.5911935335692

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