sin(-x)=cospi (уравнение)

Найду корень уравнения: sin(-x)=cospi

Вы ввели

sin(-x) = cos(pi)

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

Подробное решение

Дано уравнение
$$\sin{\left(- x \right)} = \cos{\left(\pi \right)}$$
- 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 = -86.3937977431483

x2 = -73.8274277616689

x3 = 3017.49974516717

x4 = -86.3937984749131

x5 = -36.1283160197768

x6 = 1.57079582971902

x7 = -42.4115017818136

x8 = 95.8185759975842

x9 = 70.6858358251975

x10 = 76.9690196732095

x11 = -23.5619450115115

x12 = -29.8451306226524

x13 = -80.1106125781572

x14 = -29.8451297624452

x15 = -54.9778709962906

x16 = 7.85398174307326

x17 = -29.8451300954883

x18 = 89.5353901350773

x19 = -42.4115005850814

x20 = 20.4203521477756

x21 = -10.9955738413568

x22 = 58.1194643979608

x23 = -10.9955746401247

x24 = 20.4203527610188

x25 = 89.535390888605

x26 = -98.9601689530982

x27 = -61.2610569934486

x28 = -23.5619443878998

x29 = 45.5530929823099

x30 = 89.5353893728458

x31 = 51.8362782775539

x32 = -73.8274269047688

x33 = 58.119464520069

x34 = 14.1371671100222

x35 = 51.8362788867584

x36 = 26.7035387715281

x37 = -17.2787598356363

x38 = -67.5442420547782

x39 = 58.1194636580315

x40 = -98.9601681513438

x41 = 14.1371665172699

x42 = 95.8185764110282

x43 = 1.57079769954017

x44 = -92.6769837307794

x45 = -17.2787583315643

x46 = -54.9778717966574

x47 = -4.71238942125338

x48 = -92.6769829355125

x49 = 102.101760799573

x50 = -36.1283153448593

x51 = 32.9867233134552

x52 = 64.4026499096387

x53 = -61.2610555612794

x54 = -86.3937988139119

x55 = 1.57079525114023

x56 = 1.57079657289894

x57 = 7.85398177249874

x58 = 7.85398112872719

x59 = 45.5530922954328

x60 = -73.8274272798455

x61 = -36.1283154173375

x62 = 83.252204888767

x63 = -4.71238862219396

x64 = -48.6946857788076

x65 = 39.2699077336963

x66 = 64.4026492731727

x67 = 64.4026493072124

x68 = -42.4115013226904

x69 = 45.553093730794

x70 = -80.1106131679426

x71 = 14.1371673791846

x72 = 95.8185760629547

x73 = 76.9690204681432

x74 = -48.6946865760795

x75 = 70.6858344802043

x76 = -67.5442421706656

x77 = 39.2699085343272

x78 = 20.420352160156

x79 = 51.8362789031518

x80 = -77664.8827844698

x81 = 95.8185754266891

x82 = -67.5442415371049

x83 = -17.2787590920677

x84 = 70.6858352127237

x85 = 83.2522056907544

x86 = -61.2610562447228

x87 = -23.5619449492902

x88 = 26.703537322248

x89 = -80.1106124650157

x90 = 26.7035380604159

x91 = 32.9867225164981

График