1=-sin(x-3) (уравнение)

Найду корень уравнения: 1=-sin(x-3)

Вы ввели

1 = -sin(x - 3)

$$1 = - \sin{\left(x - 3 \right)}$$

Подробное решение

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

Быстрый ответ

         pi
x1 = 3 - --
         2 

$$x_{1} = 3 - \frac{\pi}{2}$$

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

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

Численный ответ

x1 = -55.1194636160177

x2 = 57.9778709525774

x3 = 7.71238871112804

x4 = 32.8451299168822

x5 = 1.4292031994849

x6 = -29.9867225095962

x7 = 45.4115003533666

x8 = -99.1017623352632

x9 = -67.6858342078915

x10 = -23.7035370613865

x11 = 51.6946857852614

x12 = 32.8451306916205

x13 = 76.8274278452224

x14 = -48.8362783842279

x15 = -61.4026488841948

x16 = 83.1106130829475

x17 = -11.1371664621273

x18 = -36.2699079966371

x19 = 64.2610564153327

x20 = 76.8274270742491

x21 = -48.8362785261356

x22 = -23.7035375869477

x23 = 39.1283151217938

x24 = -73.9690196445572

x25 = -36.2699086790841

x26 = 20.2787600846985

x27 = -99.1017615547492

x28 = -29.9867233383951

x29 = 26.5619452777683

x30 = -73.9690204831148

x31 = 13.995574624056

x32 = 51.6946863207864

x33 = -67.6858347480276

x34 = -80.2522051555355

x35 = 51.694685622629

x36 = 265.322986748881

x37 = 1.42920397806708

x38 = 95.676982852026

x39 = 7.71238916213358

x40 = 64.2610567369989

x41 = 70.544241890842

x42 = 64.2610572303395

x43 = -4.85398203405799

x44 = -4.85398122839682

x45 = -48.8362791898048

x46 = -80.2522058295816

x47 = 13.9955757402041

x48 = -11.1371672404073

x49 = 26.5619447322855

x50 = -55.1194643976182

x51 = 95.6769834793294

x52 = 70.5442419059448

x53 = -2449.01306604989

x54 = 20.2787592836164

x55 = -92.8185763454445

x56 = 20.2787595746721

x57 = 39.1283159273289

x58 = -86.535391107832

x59 = -29.9867228802502

x60 = -17.4203517330488

x61 = 89.3937982924385

x62 = 57.9778714613053

x63 = 26.5619454178827

x64 = 95.676982773828

x65 = -80.2522054570839

x66 = 259.039799833629

x67 = 45.4115011352952

x68 = -42.5530931792452

x69 = 89.3937975073926

x70 = -86.5353903366411

x71 = -42.5530939542492

x72 = 57.9778717562782

x73 = 83.1106122777487

x74 = 13.995574292737

x75 = -99.1017607700479

x76 = 101.960168098772

x77 = -61.4026495845871

x78 = 7.71238847165566

x79 = -61.4026488418777

x80 = -67.6858349747617

x81 = -17.4203517860366

x82 = -17.4203524261899

x83 = -23.7035378464676

x84 = -92.8185755401626

x85 = -36.2699083698423

x86 = 13.9955738068458

x87 = 70.5442423491557

x88 = 70.5442425685927

x89 = -73.9690200612747

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