8sinx=7 (уравнение)

Найду корень уравнения: 8sinx=7

Вы ввели

8*sin(x) = 7

$$8 \sin{\left(x \right)} = 7$$

Подробное решение

Дано уравнение
$$8 \sin{\left(x \right)} = 7$$
- это простейшее тригонометрическое ур-ние

Разделим обе части ур-ния на 8

Ур-ние превратится в
$$\sin{\left(x \right)} = \frac{7}{8}$$
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{7}{8} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{7}{8} \right)} + \pi$$
Или
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{7}{8} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{7}{8} \right)} + \pi$$
, где n - любое целое число

Быстрый ответ

x1 = pi - asin(7/8)

$$x_{1} = \pi - \operatorname{asin}{\left(\frac{7}{8} \right)}$$

x2 = asin(7/8)

$$x_{2} = \operatorname{asin}{\left(\frac{7}{8} \right)}$$

Сумма и произведение корней

сумма

0 + pi - asin(7/8) + asin(7/8)

$$\operatorname{asin}{\left(\frac{7}{8} \right)} + \left(0 + \left(\pi - \operatorname{asin}{\left(\frac{7}{8} \right)}\right)\right)$$

=

pi

$$\pi$$

произведение

1*(pi - asin(7/8))*asin(7/8)

$$1 \left(\pi - \operatorname{asin}{\left(\frac{7}{8} \right)}\right) \operatorname{asin}{\left(\frac{7}{8} \right)}$$

=

(pi - asin(7/8))*asin(7/8)

$$\left(\pi - \operatorname{asin}{\left(\frac{7}{8} \right)}\right) \operatorname{asin}{\left(\frac{7}{8} \right)}$$

Численный ответ

x1 = 52.3416392945157

x2 = -73.322066849076

x3 = -36.6336760265668

x4 = 95.3132154242045

x5 = -16.7733990844597

x6 = 13.6318064308699

x7 = 7452.9232101315

x8 = -60.7556962347168

x9 = 83.7575658304137

x10 = 7.34862112369033

x11 = -10.4902137772801

x12 = 2.07615683707905

x13 = -61.7664172552851

x14 = -74.3327878696443

x15 = -104.737993384974

x16 = -49.200046640926

x17 = -68.0496025624647

x18 = -839.870674324986

x19 = 101.596400731384

x20 = -79.6052521562556

x21 = 58.6248246016953

x22 = 38.7645476595883

x23 = -92.1716227706147

x24 = 89.0300301170249

x25 = 70.1804741954862

x26 = 20.9257127586178

x27 = -17.784120105028

x28 = -5.21774949066885

x29 = 45.0477329667678

x30 = 77.4743805232341

x31 = 90.0407511375933

x32 = 71.1911952160545

x33 = -4.20702847010053

x34 = -86.8991584840035

x35 = 1.06543581651074

x36 = -42.9168613337464

x37 = 26.1981770452291

x38 = 39.7752686801566

x39 = -48.1893256203576

x40 = -54.4725109275372

x41 = 8.35934214425864

x42 = 96.3239364447729

x43 = -85.8884374634352

x44 = 33.492083372977

x45 = 27.2088980657974

x46 = -99.4655290983626

x47 = -11.5009347978484

x48 = 76.4636595026658

x49 = 64.9080099088749

x50 = 46.0584539873362

x51 = 63.8972888883066

x52 = 19.9149917380495

x53 = -41.906140313178

x54 = 43612.65465295

x55 = -55.4832319481055

x56 = -93.1823437911831

x57 = 32.4813623524087

x58 = 82.7468448098454

x59 = -24.0673054122076

x60 = -67.0388815418964

x61 = 57.614103581127

x62 = -30.3504907193872

x63 = -80.6159731768239

x64 = -98.4548080777943

x65 = -35.6229550059985

x66 = 1012.65827027242

x67 = 14.6425274514382

x68 = -23.0565843916393

x69 = 51.3309182739474

x70 = -29.3397696988189

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