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)

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

=

atan(5)

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

произведение

1*atan(5)

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

=

atan(5)

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

Численный ответ

x1 = -89.732786187159

x2 = 15146.9915837233

x3 = 70.4884391459205

x4 = -52.0336743440815

x5 = 5618.5410653855

x6 = -33.1841184225427

x7 = -45.7504890369019

x8 = 51.6388832243817

x9 = 17.081364034894

x10 = -36.3257110761325

x11 = 32.7893273028429

x12 = -20.6177478081835

x13 = 79.9132171066898

x14 = -1.76819188664478

x15 = 86.1964024138694

x16 = -70.8832302656202

x17 = 23.3645493420736

x18 = 48.4972905707919

x19 = -23.7593404617733

x20 = 92.479587721049

x21 = -11.1929698474142

x22 = -58.3168596512611

x23 = 73.6300317995103

x24 = 10.7981787277144

x25 = -64.6000449584406

x26 = -42.6088963833121

x27 = -61.4584523048509

x28 = -92.8743788407488

x29 = -67.7416376120304

x30 = -14.3345625010039

x31 = -99.1575641479284

x32 = 61.0636611851511

x33 = -48.8920816904917

x34 = 35.9309199564327

x35 = 76.7716244531001

x36 = 1.37340076694502

x37 = 7.6565860741246

x38 = 67.3468464923307

x39 = -26.9009331153631

x40 = -80.3080082263896

x41 = -17.4761551545937

x42 = 98.7627730282286

x43 = 54.7804758779715

x44 = -1201.85658555795

x45 = -77.1664155727998

x46 = -4.90978454023457

x47 = -30.0425257689529

x48 = -39.4673037297223

x49 = 39.0725126100225

x50 = 64.2052538387409

x51 = 4.51499342053481

x52 = 95.6211803746388

x53 = 20.2229566884838

x54 = -55.1752669976713

x55 = 29.6477346492532

x56 = -74.02482291921

x57 = -8.05137719382436

x58 = 42.2141052636123

x59 = 45.3556979172021

x60 = 89.3379950674592

x61 = 57.9220685315613

x62 = 13.9397713813042

x63 = -86.5911935335692

x64 = 83.0548097602796

x65 = 26.5061419956634

x66 = -96.0159714943386

x67 = -83.4496008799794

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