sin(pi+x)=-1 (уравнение)

Найду корень уравнения: sin(pi+x)=-1

Вы ввели

sin(pi + x) = -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
$$x = 2 \pi n + \frac{\pi}{2}$$
$$x = 2 \pi n + \frac{\pi}{2}$$
, где n - любое целое число

Быстрый ответ

     pi
x1 = --
     2 

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

Сумма и произведение корней

сумма

    pi
0 + --
    2 

$$0 + \frac{\pi}{2}$$

=

pi
--
2 

$$\frac{\pi}{2}$$

произведение

  pi
1*--
  2 

$$1 \frac{\pi}{2}$$

=

pi
--
2 

$$\frac{\pi}{2}$$

Численный ответ

x1 = -36.1283160197768

x2 = 70.6858358251975

x3 = -4.71238942125338

x4 = -98.9601681513438

x5 = -67.5442420547782

x6 = -92.6769829355125

x7 = 70.6858352127237

x8 = -80.1106125781572

x9 = 45.5530929823099

x10 = 76.9690204681432

x11 = -10.9955738413568

x12 = 45.5530922954328

x13 = -29.8451297624452

x14 = -73.8274272798455

x15 = 26.7035387715281

x16 = -4.71238862219396

x17 = 70.6858344802043

x18 = 51.8362782775539

x19 = -42.4115005850814

x20 = 89.5353901350773

x21 = -86.3937988139119

x22 = 64.4026492731727

x23 = -36.1283154173375

x24 = -10.9955746401247

x25 = 26.7035380604159

x26 = 20.4203527610188

x27 = 26.703537322248

x28 = 58.1194636580315

x29 = 1.57079657289894

x30 = -17.2787598356363

x31 = -23.5619443878998

x32 = -36.1283153448593

x33 = 1.57079582971902

x34 = 1.57079769954017

x35 = 39.2699085343272

x36 = -17.2787583315643

x37 = -92.6769837307794

x38 = 102.101760799573

x39 = 14.1371665172699

x40 = 89.535390888605

x41 = -23.5619449492902

x42 = 95.8185764110282

x43 = 45.553093730794

x44 = -80.1106124650157

x45 = -67.5442421706656

x46 = 83.2522056907544

x47 = -73.8274269047688

x48 = -61.2610562447228

x49 = 7.85398177249874

x50 = 64.4026499096387

x51 = 32.9867225164981

x52 = -23.5619450115115

x53 = 89.5353893728458

x54 = 14.1371673791846

x55 = -73.8274277616689

x56 = 7.85398112872719

x57 = 95.8185754266891

x58 = 51.8362788867584

x59 = -86.3937984749131

x60 = -42.4115013226904

x61 = -67.5442415371049

x62 = 95.8185759975842

x63 = 51.8362789031518

x64 = -80.1106131679426

x65 = 64.4026493072124

x66 = 58.119464520069

x67 = 58.1194643979608

x68 = 20.4203521477756

x69 = -61.2610569934486

x70 = -61.2610555612794

x71 = 7.85398174307326

x72 = 39.2699077336963

x73 = -48.6946857788076

x74 = -29.8451300954883

x75 = -17.2787590920677

x76 = -29.8451306226524

x77 = 83.252204888767

x78 = -54.9778709962906

x79 = 3017.49974516717

x80 = -98.9601689530982

x81 = 95.8185760629547

x82 = -42.4115017818136

x83 = -77664.8827844698

x84 = 14.1371671100222

x85 = -48.6946865760795

x86 = -86.3937977431483

x87 = 1.57079525114023

x88 = 20.420352160156

x89 = 76.9690196732095

x90 = 32.9867233134552

x91 = -54.9778717966574

График