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)

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

x2 = -asin(4/5)

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

Сумма и произведение корней

сумма

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

$$- \operatorname{asin}{\left(\frac{4}{5} \right)} + \left(0 + \left(\operatorname{asin}{\left(\frac{4}{5} \right)} + \pi\right)\right)$$

=

pi

$$\pi$$

произведение

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

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

=

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

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

Численный ответ

x1 = -51.1927776754383

x2 = -33.6302239714861

x3 = -58.7629652002045

x4 = -19.7768511395404

x5 = 85.750296864926

x6 = 93.3204843896922

x7 = 17.9222607035371

x8 = 5.35589008917797

x9 = 24.2054460107167

x10 = -88.8918895185158

x11 = -1748.93981283151

x12 = -70.0423335969771

x13 = 10.352073178771

x14 = 3585.48451296396

x15 = -7.2104805251812

x16 = 4.06888787159141

x17 = 35.4848144074893

x18 = 2989.86891099948

x19 = 99.6036696968718

x20 = 87.0372990825126

x21 = 68.1877431609738

x22 = 438.895676284569

x23 = -44.9095923682587

x24 = 61.9045578537943

x25 = -82.6087042113362

x26 = 36.7718166250759

x27 = -13.4936658323608

x28 = -21.0638533571269

x29 = -71.3293358145636

x30 = -38.6264070610791

x31 = -46.1965945858453

x32 = 29.2016291003098

x33 = 55.6213725466147

x34 = 43.0550019322555

x35 = -171.860300729437

x36 = -8.49748274276777

x37 = -57.4759629826179

x38 = -14.7806680499474

x39 = 48.0511850218485

x40 = -0.927295218001612

x41 = -90.1788917361024

x42 = 41.7679997146689

x43 = -76.3255189041567

x44 = -39.9134092786657

x45 = -101.458260132875

x46 = -214.555595662108

x47 = -52.4797798930249

x48 = 80.754113775333

x49 = -96.462077043282

x50 = -77.6125211217432

x51 = 11.6390753963576

x52 = 74.4709284681534

x53 = 49.3381872394351

x54 = 92.0334821721056

x55 = 22.9184437931302

x56 = 60.6175556362077

x57 = 30.4886313178963

x58 = 66.9007409433873

x59 = -27.3470386643065

x60 = -12894.0235455505

x61 = 54.3343703290281

x62 = 79.4671115577464

x63 = -32.3432217538995

x64 = 16.6352584859506

x65 = -83.8957064289228

x66 = -65.046150507384

x67 = 98.3166674792852

x68 = -26.06003644672

x69 = -63.7591482897975

x70 = -2.21429743558818

x71 = 73.1839262505669

x72 = -95.1750748256954

График