sin(x)=4/9 (уравнение)

Найду корень уравнения: sin(x)=4/9

Вы ввели

sin(x) = 4/9

$$\sin{\left(x \right)} = \frac{4}{9}$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = \frac{4}{9}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{4}{9} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{4}{9} \right)} + \pi$$
Или
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{4}{9} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{4}{9} \right)} + \pi$$
, где n - любое целое число

Быстрый ответ

x1 = pi - asin(4/9)

$$x_{1} = \pi - \operatorname{asin}{\left(\frac{4}{9} \right)}$$

x2 = asin(4/9)

$$x_{2} = \operatorname{asin}{\left(\frac{4}{9} \right)}$$

Сумма и произведение корней

сумма

pi - asin(4/9) + asin(4/9)

$$\operatorname{asin}{\left(\frac{4}{9} \right)} + \left(\pi - \operatorname{asin}{\left(\frac{4}{9} \right)}\right)$$

=

pi

$$\pi$$

произведение

(pi - asin(4/9))*asin(4/9)

$$\left(\pi - \operatorname{asin}{\left(\frac{4}{9} \right)}\right) \operatorname{asin}{\left(\frac{4}{9} \right)}$$

=

(pi - asin(4/9))*asin(4/9)

$$\left(\pi - \operatorname{asin}{\left(\frac{4}{9} \right)}\right) \operatorname{asin}{\left(\frac{4}{9} \right)}$$

Численный ответ

x1 = -854.052647784742

x2 = -22.4517025668099

x3 = 15.2474092762676

x4 = 19.3101099132201

x5 = -74.9376696944737

x6 = 63.2924070634772

x7 = -53.8676291027078

x8 = -62.3712990801145

x9 = -5.82263131549826

x10 = 59.2297064265247

x11 = 75.8587776778364

x12 = 96.9288182696023

x13 = -79.0003703314262

x14 = 46.6633358121656

x15 = -28.7348878739895

x16 = -60.1508144098874

x17 = 78.0792623480635

x18 = -49.8049284657554

x19 = -56.088113772935

x20 = -97.8499262529649

x21 = -43.5217431585758

x22 = -100.070410923192

x23 = 69.5755923706568

x24 = 34.0969651978064

x25 = 71.7960770408839

x26 = -30.9553725442166

x27 = -66.433999717067

x28 = 57.0092217562976

x29 = 84.3624476552431

x30 = 82.141962985016

x31 = 2.68103866190847

x32 = 65.5128917337043

x33 = -87.5040403088329

x34 = -68.6544843872941

x35 = 21.5305945834472

x36 = -12.1058166226779

x37 = -47.5844437955282

x38 = 25.5932952203997

x39 = 31.8764805275793

x40 = -41.3012584883486

x41 = -16.1685172596303

x42 = 13.0269246060405

x43 = 40.380150504986

x44 = 6.74373929886091

x45 = 44.4428511419384

x46 = 88.4251482921955

x47 = 52.9465211193452

x48 = 50.726036449118

x49 = 38.1596658347588

x50 = -9.8853319524507

x51 = -93.7872256160125

x52 = 94.7083335993751

x53 = 8.96422396908806

x54 = -37.2385578513962

x55 = -18.3890019298574

x56 = -24.672187237037

x57 = 90.6456329624227

x58 = 0.460553991681322

x59 = -91.5667409457853

x60 = -35.0180731811691

x61 = 27.8137798906268

x62 = -72.7171850242466

x63 = 100.991518906555

x64 = -3.60214664527112

x65 = -85.2835556386057

x66 = -225.734117066784

x67 = -81.2208550016533

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