sin(z)=-1 (уравнение)

Найду корень уравнения: sin(z)=-1

Вы ввели

sin(z) = -1

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

Подробное решение

Дано уравнение
$$\sin{\left(z \right)} = -1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$z = 2 \pi n + \operatorname{asin}{\left(-1 \right)}$$
$$z = 2 \pi n - \operatorname{asin}{\left(-1 \right)} + \pi$$
Или
$$z = 2 \pi n - \frac{\pi}{2}$$
$$z = 2 \pi n + \frac{3 \pi}{2}$$
, где n - любое целое число

Быстрый ответ

     -pi 
z1 = ----
      2  

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

     3*pi
z2 = ----
      2  

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

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

z1 = -20.420353265929

z2 = -45.5530935025548

z3 = -70.6858351534454

z4 = -70.6858343571487

z5 = 86.3937978309099

z6 = 98.9601692809083

z7 = 23.5619451518571

z8 = -14.1371674455661

z9 = 61.2610571125526

z10 = 67.54424230971

z11 = 42.4115007274741

z12 = -39.2699076683741

z13 = -1.57079639503667

z14 = -89.5353901118113

z15 = 48.6946859012172

z16 = 4.71238874329685

z17 = 80.1106130902139

z18 = -83.2522048211133

z19 = -51.8362783335234

z20 = 48.6946866365921

z21 = 67.5442408278864

z22 = 92.6769830592094

z23 = 10.9955739381756

z24 = -45.5530935911043

z25 = -45.5530929624673

z26 = 86.3937984838325

z27 = 17.2787591562062

z28 = 98.9601690454399

z29 = -58.1194639976905

z30 = -32.9867232184024

z31 = -89.535390750197

z32 = 23.5619444059921

z33 = -14.1371668370864

z34 = 92.6769837888103

z35 = 36.1283159497235

z36 = -39.2699084145515

z37 = 73.8274274830848

z38 = -58.1194645939029

z39 = -58.1194639046052

z40 = 73.8274268520838

z41 = 67.5442415586719

z42 = -26.7035372004893

z43 = -95.818575476176

z44 = -76.9690195738024

z45 = 92.6769843439965

z46 = -102.101761026058

z47 = -20.4203527465087

z48 = 4.71239022926564

z49 = 42.4115013353669

z50 = -26.7035379986821

z51 = 29.8451297031011

z52 = -70.6858331259916

z53 = -95.8185758680502

z54 = -64.4026498988255

z55 = -39.2699069219675

z56 = 17.2787599560783

z57 = -51.8362786893284

z58 = -7.85398119154045

z59 = -83.2522055723275

z60 = 36.1283157235346

z61 = 73.8274274426229

z62 = -20.4203520060805

z63 = -7.85398205280014

z64 = -7.85398149665124

z65 = 48.6946873020308

z66 = 98.9601682515978

z67 = -83.2522042893833

z68 = 42.4115007162407

z69 = 80.1106131368654

z70 = 86.3937978869933

z71 = 10.9955747360645

z72 = -1.57079643188553

z73 = 23.5619437708833

z74 = 36.1283150875497

z75 = 61.2610563112167

z76 = 29.845130330036

z77 = -76.9690203748894

z78 = -64.4026491641039

z79 = -64.4026502975618

z80 = -89.5353906059052

z81 = 538.783139388541

z82 = 54.9778710948428

z83 = 4.7123894841958

z84 = 80.1106122287081

z85 = 48.6946870830469

z86 = -51.8362791922783

z87 = -14.1371667858125

z88 = 29.8451303231501

z89 = -32.9867224188086

z90 = -1.57079581340397

z91 = -95.8185763308148

z92 = 54.9778718908148

График