2sinx=5cosx (уравнение)

Найду корень уравнения: 2sinx=5cosx

Вы ввели

2*sin(x) = 5*cos(x)

$$2 \sin{\left(x \right)} = 5 \cos{\left(x \right)}$$

Подробное решение

Дано уравнение
$$2 \sin{\left(x \right)} = 5 \cos{\left(x \right)}$$
преобразуем:
$$\frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}} = 5$$
или
$$2 \tan{\left(x \right)} = 5$$
- это простейшее тригонометрическое ур-ние

Разделим обе части ур-ния на 2

Ур-ние превратится в
$$\tan{\left(x \right)} = - \frac{5}{2}$$
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{atan}{\left(- \frac{5}{2} \right)}$$
Или
$$x = \pi n - \operatorname{atan}{\left(\frac{5}{2} \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = atan(5/2)

$$x_{1} = \operatorname{atan}{\left(\frac{5}{2} \right)}$$

Сумма и произведение корней

сумма

0 + atan(5/2)

$$0 + \operatorname{atan}{\left(\frac{5}{2} \right)}$$

=

atan(5/2)

$$\operatorname{atan}{\left(\frac{5}{2} \right)}$$

произведение

1*atan(5/2)

$$1 \operatorname{atan}{\left(\frac{5}{2} \right)}$$

=

atan(5/2)

$$\operatorname{atan}{\left(\frac{5}{2} \right)}$$

Численный ответ

x1 = -14.5176733182664

x2 = 95.4380695573763

x3 = 26.3230311784009

x4 = 67.1637356750682

x5 = -42.7920072005746

x6 = 79.7301062894274

x7 = 98.5796622109661

x8 = 86.0132915966069

x9 = 1.19028994968253

x10 = 32.6062164855805

x11 = -71.0663410828827

x12 = 57.7389577142988

x13 = 42.0309944463498

x14 = -102.482267618781

x15 = 60.8805503678886

x16 = -17.6592659718562

x17 = -83.6327116972419

x18 = -93.0574896580113

x19 = -58.4999704685235

x20 = -99.3406749651909

x21 = -20.800858625446

x22 = 51.4557724071192

x23 = 29.4646238319907

x24 = -45.9335998541644

x25 = 38.88940179276

x26 = 92.2964769037865

x27 = 10.6150679104519

x28 = 481.853965948921

x29 = -23.9424512790358

x30 = -61.6415631221133

x31 = -74.2079337364725

x32 = 434.730076145074

x33 = 82.8716989430172

x34 = -55.3583778149337

x35 = -27.0840439326256

x36 = 13.7566605640417

x37 = -11.3760806646766

x38 = -89.9158970044215

x39 = 16.8982532176315

x40 = -30.2256365862154

x41 = -36.508821893395

x42 = 5665.48184437208

x43 = 48.3141797535294

x44 = 4.33188260327232

x45 = -96.1990823116011

x46 = -67.9247484292929

x47 = 54.597365060709

x48 = -77.3495263900623

x49 = 20.0398458712213

x50 = -501.464534624684

x51 = -5.09289535749705

x52 = -8.23448801108685

x53 = -49.0751925077542

x54 = 7.47347525686212

x55 = 73.4469209822478

x56 = -39.6504145469848

x57 = -209.296417840834

x58 = -52.216785161344

x59 = 5379.59691289541

x60 = -86.7743043508317

x61 = 70.305328328658

x62 = -80.4911190436521

x63 = 76.5885136358376

x64 = 89.1548842501967

x65 = -33.3672292398052

x66 = 45.1725870999396

x67 = 64.0221430214784

x68 = 35.7478091391703

x69 = -64.7831557757031

x70 = -1.95130270390726

x71 = 23.1814385248111

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