sin(x)=4/5 (уравнение)

Найду корень уравнения: sin(x)=4/5

Вы ввели

sin(x) = 4/5

$$\sin{\left(x \right)} = \frac{4}{5}$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = \frac{4}{5}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{4}{5} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{4}{5} \right)} + \pi$$
Или
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{4}{5} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{4}{5} \right)} + \pi$$
, где n - любое целое число

Быстрый ответ

x1 = pi - asin(4/5)

$$x_{1} = \pi - \operatorname{asin}{\left(\frac{4}{5} \right)}$$

x2 = asin(4/5)

$$x_{2} = \operatorname{asin}{\left(\frac{4}{5} \right)}$$

Сумма и произведение корней

сумма

pi - asin(4/5) + asin(4/5)

$$\operatorname{asin}{\left(\frac{4}{5} \right)} + \left(\pi - \operatorname{asin}{\left(\frac{4}{5} \right)}\right)$$

=

pi

$$\pi$$

произведение

(pi - asin(4/5))*asin(4/5)

$$\left(\pi - \operatorname{asin}{\left(\frac{4}{5} \right)}\right) \operatorname{asin}{\left(\frac{4}{5} \right)}$$

=

(pi - asin(4/5))*asin(4/5)

$$\left(\pi - \operatorname{asin}{\left(\frac{4}{5} \right)}\right) \operatorname{asin}{\left(\frac{4}{5} \right)}$$

Численный ответ

x1 = 77.6125211217432

x2 = -4.06888787159141

x3 = 83.8957064289228

x4 = 46.1965945858453

x5 = 90.1788917361024

x6 = -1015.6617223275

x7 = 38.6264070610791

x8 = -68.1877431609738

x9 = 82.6087042113362

x10 = -17.9222607035371

x11 = 101.458260132875

x12 = -11.6390753963576

x13 = -35.4848144074893

x14 = 96.462077043282

x15 = 58.7629652002045

x16 = 33.6302239714861

x17 = -61.9045578537943

x18 = -593494.903448134

x19 = -73.1839262505669

x20 = -24.2054460107167

x21 = -41.7679997146689

x22 = 7.2104805251812

x23 = -99.6036696968718

x24 = 52.4797798930249

x25 = 26.06003644672

x26 = 88.8918895185158

x27 = 21.0638533571269

x28 = -54.3343703290281

x29 = 70.0423335969771

x30 = -80.754113775333

x31 = -55.6213725466147

x32 = -36.7718166250759

x33 = -60.6175556362077

x34 = 580.26734569611

x35 = -87.0372990825126

x36 = -74.4709284681534

x37 = -49.3381872394351

x38 = -48.0511850218485

x39 = 8.49748274276777

x40 = 2.21429743558818

x41 = -30.4886313178963

x42 = -29.2016291003098

x43 = -22.9184437931302

x44 = -93.3204843896922

x45 = -5.35589008917797

x46 = 44.9095923682587

x47 = 14.7806680499474

x48 = 32.3432217538995

x49 = 71.3293358145636

x50 = -85.750296864926

x51 = 0.927295218001612

x52 = -43.0550019322555

x53 = 51.1927776754383

x54 = -16.6352584859506

x55 = 13.4936658323608

x56 = -10.352073178771

x57 = 57.4759629826179

x58 = -564.559382428161

x59 = 76.3255189041567

x60 = -66.9007409433873

x61 = -92.0334821721056

x62 = -2787.51997895215

x63 = 65.046150507384

x64 = -98.3166674792852

x65 = 27.3470386643065

x66 = 39.9134092786657

x67 = -79.4671115577464

x68 = 63.7591482897975

x69 = 19.7768511395404

x70 = 95.1750748256954

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