5sinx=cosx (уравнение)

Найду корень уравнения: 5sinx=cosx

Вы ввели

5*sin(x) = cos(x)

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

Подробное решение

Дано уравнение
$$5 \sin{\left(x \right)} = \cos{\left(x \right)}$$
преобразуем:
$$\frac{5 \sin{\left(x \right)}}{\cos{\left(x \right)}} = 1$$
или
$$5 \tan{\left(x \right)} = 1$$
- это простейшее тригонометрическое ур-ние

Разделим обе части ур-ния на 5

Ур-ние превратится в
$$\tan{\left(x \right)} = - \frac{1}{5}$$
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{atan}{\left(- \frac{1}{5} \right)}$$
Или
$$x = \pi n - \operatorname{atan}{\left(\frac{1}{5} \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = atan(1/5)

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

Сумма и произведение корней

сумма

0 + atan(1/5)

$$0 + \operatorname{atan}{\left(\frac{1}{5} \right)}$$

=

atan(1/5)

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

произведение

1*atan(1/5)

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

=

atan(1/5)

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

Численный ответ

x1 = -78.342420779895

x2 = -43.7849015904072

x3 = 94.4451751675437

x4 = 85.0203972067743

x5 = 66.1708412852355

x6 = 25.3301367885682

x7 = -56.3512722047664

x8 = -65.7760501655358

x9 = 100.728360474723

x10 = -72.0592354727154

x11 = 12.7637661742091

x12 = -50.0680868975868

x13 = -12.3689750545093

x14 = 59.887655978056

x15 = 97.5867678211335

x16 = -24.9353456688685

x17 = -53.2096795511766

x18 = -100.333569355023

x19 = 34.7549147493376

x20 = -28.0769383224583

x21 = 15.9053588277988

x22 = 69.3124339388253

x23 = -2.94419709373991

x24 = 41.0381000565172

x25 = 53.6044706708764

x26 = -68.9176428191256

x27 = 72.4540265924151

x28 = 22.1885441349784

x29 = -22292.5440743133

x30 = 3.33898821343967

x31 = 597.099999741911

x32 = 63.0292486316457

x33 = -6.08578974732971

x34 = 88.1619898603641

x35 = 0.197395559849881

x36 = -84.6256060870745

x37 = -90.9087913942541

x38 = 28.471729442158

x39 = 81.8788045531845

x40 = 56.7460633244662

x41 = 37.8965074029274

x42 = -97.1919767014337

x43 = 78.7372118995947

x44 = -62.634457511946

x45 = -40.6433089368174

x46 = 47.3212853636968

x47 = -94.0503840478439

x48 = 6.48058086702947

x49 = -46.926494243997

x50 = -9.2273824009195

x51 = -21.7937530152787

x52 = 91.3035825139539

x53 = 31.6133220957478

x54 = 50.4628780172866

x55 = 9.62217352061926

x56 = -18.6521603616889

x57 = -37.5017162832276

x58 = -31.2185309760481

x59 = 44.179692710107

x60 = -15.5105677080991

x61 = -87.7671987406643

x62 = -59.4928648583562

x63 = -75.2008281263052

x64 = -34.3601236296378

x65 = 19.0469514813886

x66 = 75.5956192460049

x67 = -81.4840134334847

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