sin(x-pi)=1 (уравнение)

Найду корень уравнения: sin(x-pi)=1

Вы ввели

sin(x - pi) = 1

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

Подробное решение

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

Разделим обе части ур-ния на -1

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 = -14.1371667858125

x2 = -7.85398119154045

x3 = -39.2699084145515

x4 = 4.71239022926564

x5 = -70.6858331259916

x6 = -51.8362786893284

x7 = -89.5353906059052

x8 = -76.9690203748894

x9 = 67.5442415586719

x10 = -58.1194639976905

x11 = -51.8362783335234

x12 = 73.8274274426229

x13 = -1.57079581340397

x14 = 36.1283159497235

x15 = -20.4203527465087

x16 = 86.3937984838325

x17 = 80.1106131368654

x18 = 17.2787591562062

x19 = -45.5530935911043

x20 = -58.1194639046052

x21 = 23.5619451518571

x22 = -89.535390750197

x23 = -32.9867232184024

x24 = -7.85398205280014

x25 = 80.1106122287081

x26 = 67.54424230971

x27 = 98.9601692809083

x28 = -58.1194645939029

x29 = 29.8451303231501

x30 = -1.57079643188553

x31 = -1.57079639503667

x32 = -70.6858343571487

x33 = 61.2610563112167

x34 = -95.8185758680502

x35 = 29.845130330036

x36 = -64.4026502975618

x37 = 98.9601690454399

x38 = 29.8451297031011

x39 = 61.2610571125526

x40 = 48.6946859012172

x41 = 92.6769837888103

x42 = 42.4115013353669

x43 = 36.1283150875497

x44 = 98.9601682515978

x45 = -83.2522042893833

x46 = 42.4115007162407

x47 = -39.2699076683741

x48 = -64.4026498988255

x49 = -7.85398149665124

x50 = -45.5530935025548

x51 = -14.1371674455661

x52 = 48.6946870830469

x53 = -20.4203520060805

x54 = 23.5619437708833

x55 = -83.2522048211133

x56 = 538.783139388541

x57 = -76.9690195738024

x58 = 48.6946873020308

x59 = -83.2522055723275

x60 = -51.8362791922783

x61 = -102.101761026058

x62 = 42.4115007274741

x63 = -14.1371668370864

x64 = 54.9778710948428

x65 = 80.1106130902139

x66 = -32.9867224188086

x67 = 36.1283157235346

x68 = 73.8274274830848

x69 = 17.2787599560783

x70 = 4.71238874329685

x71 = -95.8185763308148

x72 = 48.6946866365921

x73 = 10.9955747360645

x74 = -39.2699069219675

x75 = -89.5353901118113

x76 = -20.420353265929

x77 = -64.4026491641039

x78 = -26.7035379986821

x79 = 67.5442408278864

x80 = 86.3937978309099

x81 = 92.6769830592094

x82 = -70.6858351534454

x83 = -45.5530929624673

x84 = 54.9778718908148

x85 = 92.6769843439965

x86 = 10.9955739381756

x87 = -95.818575476176

x88 = 4.7123894841958

x89 = 73.8274268520838

x90 = 23.5619444059921

x91 = -26.7035372004893

x92 = 86.3937978869933

График