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)

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

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)

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

=

pi

$$\pi$$

произведение

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

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

=

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

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

Численный ответ

x1 = 4.26136216858843

x2 = -39.7209349816687

x3 = -63.9516225867945

x4 = -2.02182313859116

x5 = -57.6684372796149

x6 = 48.2436593188455

x7 = 17.7297864065401

x8 = -76.5179932011537

x9 = 93.1280100926952

x10 = 23.1109180901272

x11 = -82.8011785083333

x12 = -19.9693254365374

x13 = -45.1020666652557

x14 = 98.5091417762822

x15 = 651.429448808086

x16 = -32.5356960508966

x17 = -58.5704909032074

x18 = 73.3764005475639

x19 = 3610.80972848967

x20 = -14.5881937529503

x21 = 67.0932152403843

x22 = -20.8713790601299

x23 = 99.4111953998747

x24 = 67.9952688639768

x25 = -8.30500844577075

x26 = 54.5268446260251

x27 = -26.252510743717

x28 = -64.853676210387

x29 = -13.6861401293578

x30 = -95.3675491226924

x31 = 11.4466010993605

x32 = -51.3852519724353

x33 = -52.2873055960278

x34 = 74.2784541711564

x35 = 5.16341579218095

x36 = -33.4377496744891

x37 = -71.1368615175666

x38 = 10.544547475768

x39 = 16.8277327829476

x40 = 14367.6229743811

x41 = 61.7120835567972

x42 = 36.5793423280789

x43 = -46.0041202888483

x44 = 92.2259564691026

x45 = -89.0843638155128

x46 = 41.9604740116659

x47 = -140.251899896542

x48 = 35.6772887044864

x49 = 86.8448247855156

x50 = -38.8188813580762

x51 = -101.650734429872

x52 = 49.1457129424381

x53 = -89.9864174391054

x54 = 60.8100299332047

x55 = -83.7032321319258

x56 = 30.2961570208993

x57 = -96.269602746285

x58 = -102.552788053465

x59 = -1.11976951499863

x60 = 80.561639478336

x61 = -77.4200468247462

x62 = 400.102036520902

x63 = 55.4288982496176

x64 = -120.500290351411

x65 = -1496.51787262374

x66 = -27.1545643673095

x67 = 42.8625276352585

x68 = -7.40295482217822

x69 = -70.2348078939741

x70 = 79.6595858547435

x71 = 29.3941033973068

x72 = 24.0129717137197

x73 = 85.942771161923

График