sin(5π+x)=1 (уравнение)

Найду корень уравнения: sin(5π+x)=1

Вы ввели

sin(5*POST_GRBEK_SMALL_pi + x) = 1

$$\sin{\left(5 POST_{GRBEK SMALL \pi} + x \right)} = 1$$

Подробное решение

Дано уравнение
$$\sin{\left(5 POST_{GRBEK SMALL \pi} + x \right)} = 1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$5 POST_{GRBEK SMALL \pi} + x = 2 \pi n + \operatorname{asin}{\left(1 \right)}$$
$$5 POST_{GRBEK SMALL \pi} + x = 2 \pi n - \operatorname{asin}{\left(1 \right)} + \pi$$
Или
$$5 POST_{GRBEK SMALL \pi} + x = 2 \pi n + \frac{\pi}{2}$$
$$5 POST_{GRBEK SMALL \pi} + x = 2 \pi n + \frac{\pi}{2}$$
, где n - любое целое число
Перенесём
$$5 POST_{GRBEK SMALL \pi}$$
в правую часть ур-ния
с противоположным знаком, итого:
$$x = - 5 POST_{GRBEK SMALL \pi} + 2 \pi n + \frac{\pi}{2}$$
$$x = - 5 POST_{GRBEK SMALL \pi} + 2 \pi n + \frac{\pi}{2}$$

Быстрый ответ

     pi                        
x1 = -- - 5*POST_GRBEK_SMALL_pi
     2                         

$$x_{1} = - 5 POST_{GRBEK SMALL \pi} + \frac{\pi}{2}$$

Сумма и произведение корней

сумма

    pi                        
0 + -- - 5*POST_GRBEK_SMALL_pi
    2                         

$$\left(- 5 POST_{GRBEK SMALL \pi} + \frac{\pi}{2}\right) + 0$$

=

pi                        
-- - 5*POST_GRBEK_SMALL_pi
2                         

$$- 5 POST_{GRBEK SMALL \pi} + \frac{\pi}{2}$$

произведение

  /pi                        \
1*|-- - 5*POST_GRBEK_SMALL_pi|
  \2                         /

$$1 \left(- 5 POST_{GRBEK SMALL \pi} + \frac{\pi}{2}\right)$$

=

pi                        
-- - 5*POST_GRBEK_SMALL_pi
2                         

$$- 5 POST_{GRBEK SMALL \pi} + \frac{\pi}{2}$$

Численный ответ

x1 = -7.85398205280014

x2 = 73.8274268520838

x3 = -7.85398119154045

x4 = 86.3937978309099

x5 = -39.2699084145515

x6 = 48.6946873020308

x7 = -32.9867224188086

x8 = -58.1194639046052

x9 = -1.57079643188553

x10 = 23.5619444059921

x11 = 42.4115007274741

x12 = -58.1194639976905

x13 = 48.6946859012172

x14 = -70.6858331259916

x15 = -89.5353901118113

x16 = -45.5530935025548

x17 = 73.8274274830848

x18 = -26.7035379986821

x19 = 4.71238874329685

x20 = -83.2522055723275

x21 = 80.1106131368654

x22 = 54.9778718908148

x23 = -1.57079581340397

x24 = -83.2522042893833

x25 = 48.6946866365921

x26 = -1.57079639503667

x27 = -14.1371667858125

x28 = 36.1283150875497

x29 = -89.5353906059052

x30 = -76.9690203748894

x31 = -7.85398149665124

x32 = 92.6769837888103

x33 = -64.4026498988255

x34 = -102.101761026058

x35 = -76.9690195738024

x36 = 98.9601692809083

x37 = -32.9867232184024

x38 = 42.4115007162407

x39 = 54.9778710948428

x40 = 61.2610571125526

x41 = -20.4203520060805

x42 = 23.5619451518571

x43 = 29.8451303231501

x44 = -95.818575476176

x45 = -45.5530935911043

x46 = -64.4026491641039

x47 = -39.2699076683741

x48 = -83.2522048211133

x49 = -58.1194645939029

x50 = 4.71239022926564

x51 = 17.2787591562062

x52 = 36.1283157235346

x53 = -45.5530929624673

x54 = 4.7123894841958

x55 = 29.8451297031011

x56 = 23.5619437708833

x57 = 29.845130330036

x58 = 42.4115013353669

x59 = 36.1283159497235

x60 = -51.8362791922783

x61 = -95.8185758680502

x62 = 67.5442408278864

x63 = -70.6858351534454

x64 = 17.2787599560783

x65 = 80.1106122287081

x66 = 10.9955747360645

x67 = 92.6769843439965

x68 = 86.3937984838325

x69 = -14.1371674455661

x70 = 48.6946870830469

x71 = -20.4203527465087

x72 = -64.4026502975618

x73 = 538.783139388541

x74 = 61.2610563112167

x75 = -20.420353265929

x76 = 67.54424230971

x77 = 67.5442415586719

x78 = -95.8185763308148

x79 = 86.3937978869933

x80 = 98.9601690454399

x81 = -39.2699069219675

x82 = 80.1106130902139

x83 = -89.535390750197

x84 = 73.8274274426229

x85 = -70.6858343571487

x86 = -26.7035372004893

x87 = 98.9601682515978

x88 = 10.9955739381756

x89 = -14.1371668370864

x90 = 92.6769830592094

x91 = -51.8362786893284

x92 = -51.8362783335234

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