- sin(x + 2) = 1 (уравнение)

Найду корень уравнения: - sin(x + 2) = 1

Вы ввели

-sin(x + 2) = 1

$$- \sin{\left(x + 2 \right)} = 1$$

Подробное решение

Дано уравнение
$$- \sin{\left(x + 2 \right)} = 1$$
- это простейшее тригонометрическое ур-ние

Разделим обе части ур-ния на -1

Ур-ние превратится в
$$\sin{\left(x + 2 \right)} = -1$$
Это ур-ние преобразуется в
$$x + 2 = 2 \pi n + \operatorname{asin}{\left(-1 \right)}$$
$$x + 2 = 2 \pi n - \operatorname{asin}{\left(-1 \right)} + \pi$$
Или
$$x + 2 = 2 \pi n - \frac{\pi}{2}$$
$$x + 2 = 2 \pi n + \frac{3 \pi}{2}$$
, где n - любое целое число
Перенесём
$$2$$
в правую часть ур-ния
с противоположным знаком, итого:
$$x = 2 \pi n - 2 - \frac{\pi}{2}$$
$$x = 2 \pi n - 2 + \frac{3 \pi}{2}$$

Быстрый ответ

          pi
x1 = -2 - --
          2 

$$x_{1} = -2 - \frac{\pi}{2}$$

          3*pi
x2 = -2 + ----
           2  

$$x_{2} = -2 + \frac{3 \pi}{2}$$

Численный ответ

x1 = -41.2699069219675

x2 = 8.99557473606454

x3 = 40.4115013353669

x4 = 96.9601690454399

x5 = -16.1371674455661

x6 = 65.54424230971

x7 = 59.2610563112167

x8 = 71.8274274426229

x9 = -78.9690203748894

x10 = 8.99557393817556

x11 = 40.4115007274741

x12 = 27.8451297031011

x13 = 52.9778710948428

x14 = -34.9867224188086

x15 = 40.4115007162407

x16 = -66.4026491641039

x17 = -72.6858351534454

x18 = 96.9601692809083

x19 = -22.420353265929

x20 = -60.1194639976905

x21 = -3.57079643188553

x22 = -97.8185763308148

x23 = 46.6946859012172

x24 = -34.9867232184024

x25 = -47.5530935025548

x26 = 2.71238874329685

x27 = -72.6858331259916

x28 = 2.71239022926564

x29 = 15.2787599560783

x30 = 2.7123894841958

x31 = -78.9690195738024

x32 = -97.8185758680502

x33 = -53.8362783335234

x34 = 78.1106122287081

x35 = -53.8362786893284

x36 = 71.8274274830848

x37 = -41.2699084145515

x38 = 21.5619444059921

x39 = -22.4203527465087

x40 = -47.5530935911043

x41 = -9.85398205280014

x42 = -16.1371668370864

x43 = -91.5353906059052

x44 = -22.4203520060805

x45 = -91.5353901118113

x46 = 34.1283159497235

x47 = 84.3937984838325

x48 = -16.1371667858125

x49 = 52.9778718908148

x50 = 21.5619451518571

x51 = 71.8274268520838

x52 = -85.2522042893833

x53 = -91.535390750197

x54 = -9.85398149665124

x55 = 34.1283150875497

x56 = 78.1106131368654

x57 = -9.85398119154045

x58 = -28.7035379986821

x59 = -85.2522048211133

x60 = -60.1194639046052

x61 = 27.845130330036

x62 = 46.6946870830469

x63 = -72.6858343571487

x64 = -28.7035372004893

x65 = 59.2610571125526

x66 = -66.4026502975618

x67 = 90.6769837888103

x68 = -41.2699076683741

x69 = 96.9601682515978

x70 = 536.783139388541

x71 = -66.4026498988255

x72 = -85.2522055723275

x73 = -3.57079581340397

x74 = 34.1283157235346

x75 = -97.818575476176

x76 = 46.6946873020308

x77 = 90.6769843439965

x78 = 27.8451303231501

x79 = 78.1106130902139

x80 = 46.6946866365921

x81 = -47.5530929624673

x82 = 65.5442408278864

x83 = 21.5619437708833

x84 = -3.57079639503667

x85 = -53.8362791922783

x86 = 84.3937978309099

x87 = 15.2787591562062

x88 = 84.3937978869933

x89 = 90.6769830592094

x90 = -60.1194645939029

x91 = 65.5442415586719

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