sin(x)=0,9 (уравнение)

Найду корень уравнения: sin(x)=0,9

Вы ввели

sin(x) = 9/10

$$\sin{\left(x \right)} = \frac{9}{10}$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = \frac{9}{10}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{9}{10} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{9}{10} \right)} + \pi$$
Или
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{9}{10} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{9}{10} \right)} + \pi$$
, где n - любое целое число

Быстрый ответ

x1 = pi - asin(9/10)

$$x_{1} = \pi - \operatorname{asin}{\left(\frac{9}{10} \right)}$$

x2 = asin(9/10)

$$x_{2} = \operatorname{asin}{\left(\frac{9}{10} \right)}$$

Сумма и произведение корней

сумма

0 + pi - asin(9/10) + asin(9/10)

$$\operatorname{asin}{\left(\frac{9}{10} \right)} + \left(0 + \left(\pi - \operatorname{asin}{\left(\frac{9}{10} \right)}\right)\right)$$

=

pi

$$\pi$$

произведение

1*(pi - asin(9/10))*asin(9/10)

$$1 \left(\pi - \operatorname{asin}{\left(\frac{9}{10} \right)}\right) \operatorname{asin}{\left(\frac{9}{10} \right)}$$

=

(pi - asin(9/10))*asin(9/10)

$$\left(\pi - \operatorname{asin}{\left(\frac{9}{10} \right)}\right) \operatorname{asin}{\left(\frac{9}{10} \right)}$$

Численный ответ

x1 = 63.9516225867945

x2 = 82.8011785083333

x3 = -42.8625276352585

x4 = -85.942771161923

x5 = -2977.11006608813

x6 = -93.1280100926952

x7 = -74.2784541711564

x8 = -92.2259564691026

x9 = 64.853676210387

x10 = 27.1545643673095

x11 = 96.269602746285

x12 = 20.8713790601299

x13 = 52.2873055960278

x14 = -79.6595858547435

x15 = 45.1020666652557

x16 = -17.7297864065401

x17 = 89.9864174391054

x18 = -98.5091417762822

x19 = -67.0932152403843

x20 = -23.1109180901272

x21 = 14.5881937529503

x22 = -61.7120835567972

x23 = 89.0843638155128

x24 = -24.0129717137197

x25 = 33.4377496744891

x26 = -5.16341579218095

x27 = -30.2961570208993

x28 = 13.6861401293578

x29 = -49.1457129424381

x30 = -73.3764005475639

x31 = 38.8188813580762

x32 = -11.4466010993605

x33 = 51.3852519724353

x34 = -16.8277327829476

x35 = -256.490828079364

x36 = 58.5704909032074

x37 = 8.30500844577075

x38 = 39.7209349816687

x39 = 46.0041202888483

x40 = -299.571071606029

x41 = -35.6772887044864

x42 = 77.4200468247462

x43 = -99.4111953998747

x44 = 32.5356960508966

x45 = -118.260751321414

x46 = -41.9604740116659

x47 = -54.5268446260251

x48 = -55.4288982496176

x49 = -86.8448247855156

x50 = -80.561639478336

x51 = 7.40295482217822

x52 = -217.889662612694

x53 = -4.26136216858843

x54 = 83.7032321319258

x55 = 101.650734429872

x56 = -67.9952688639768

x57 = 71.1368615175666

x58 = 70.2348078939741

x59 = -60.8100299332047

x60 = 550414.435863754

x61 = -142.491438926539

x62 = 26.252510743717

x63 = 2.02182313859116

x64 = -36.5793423280789

x65 = -10.544547475768

x66 = -29.3941033973068

x67 = -48.2436593188455

x68 = 1.11976951499863

x69 = 95.3675491226924

x70 = 19.9693254365374

x71 = 76.5179932011537

x72 = 57.6684372796149

График