5*sin=-5 (уравнение)

Найду корень уравнения: 5*sin=-5

Вы ввели

5*sin(x) = -5

$$5 \sin{\left(x \right)} = -5$$

Подробное решение

Дано уравнение
$$5 \sin{\left(x \right)} = -5$$
- это простейшее тригонометрическое ур-ние

Разделим обе части ур-ния на 5

Ур-ние превратится в
$$\sin{\left(x \right)} = -1$$
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(-1 \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(-1 \right)} + \pi$$
Или
$$x = 2 \pi n - \frac{\pi}{2}$$
$$x = 2 \pi n + \frac{3 \pi}{2}$$
, где n - любое целое число

Быстрый ответ

     -pi 
x1 = ----
      2  

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

     3*pi
x2 = ----
      2  

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

Сумма и произведение корней

сумма

    pi   3*pi
0 - -- + ----
    2     2  

$$\left(- \frac{\pi}{2} + 0\right) + \frac{3 \pi}{2}$$

=

pi

$$\pi$$

произведение

  -pi  3*pi
1*----*----
   2    2  

$$\frac{3 \pi}{2} \cdot 1 \left(- \frac{\pi}{2}\right)$$

=

     2
-3*pi 
------
  4   

$$- \frac{3 \pi^{2}}{4}$$

Численный ответ

x1 = -7.85398149665124

x2 = -51.8362783335234

x3 = 67.54424230971

x4 = 23.5619451518571

x5 = -70.6858351534454

x6 = 10.9955739381756

x7 = -45.5530935911043

x8 = 29.8451297031011

x9 = 23.5619444059921

x10 = -58.1194639976905

x11 = 67.5442415586719

x12 = 98.9601682515978

x13 = 98.9601692809083

x14 = 42.4115007274741

x15 = 73.8274268520838

x16 = -64.4026498988255

x17 = -95.8185758680502

x18 = -39.2699076683741

x19 = 48.6946859012172

x20 = -76.9690203748894

x21 = -95.8185763308148

x22 = -7.85398119154045

x23 = 73.8274274426229

x24 = -83.2522055723275

x25 = -89.5353906059052

x26 = -45.5530929624673

x27 = 61.2610563112167

x28 = -7.85398205280014

x29 = 10.9955747360645

x30 = 61.2610571125526

x31 = 17.2787591562062

x32 = -51.8362791922783

x33 = 86.3937978869933

x34 = -1.57079643188553

x35 = -89.535390750197

x36 = -64.4026491641039

x37 = -58.1194645939029

x38 = 42.4115013353669

x39 = -51.8362786893284

x40 = 86.3937984838325

x41 = 80.1106130902139

x42 = 92.6769837888103

x43 = 36.1283159497235

x44 = 80.1106131368654

x45 = -1.57079639503667

x46 = -39.2699084145515

x47 = 4.7123894841958

x48 = 29.845130330036

x49 = -14.1371668370864

x50 = -76.9690195738024

x51 = -26.7035379986821

x52 = 73.8274274830848

x53 = -14.1371674455661

x54 = 86.3937978309099

x55 = -70.6858343571487

x56 = 36.1283150875497

x57 = 538.783139388541

x58 = -14.1371667858125

x59 = -32.9867232184024

x60 = -58.1194639046052

x61 = 4.71238874329685

x62 = -26.7035372004893

x63 = -95.818575476176

x64 = 54.9778710948428

x65 = -45.5530935025548

x66 = -32.9867224188086

x67 = -89.5353901118113

x68 = -20.4203527465087

x69 = 98.9601690454399

x70 = -20.4203520060805

x71 = -1.57079581340397

x72 = 17.2787599560783

x73 = -83.2522048211133

x74 = 54.9778718908148

x75 = 29.8451303231501

x76 = 48.6946866365921

x77 = 80.1106122287081

x78 = 42.4115007162407

x79 = -102.101761026058

x80 = 92.6769830592094

x81 = 36.1283157235346

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