cos(2x)+1=0 (уравнение)

Найду корень уравнения: cos(2x)+1=0

Вы ввели

cos(2*x) + 1 = 0

$$\cos{\left(2 x \right)} + 1 = 0$$

Подробное решение

Дано уравнение
$$\cos{\left(2 x \right)} + 1 = 0$$
- это простейшее тригонометрическое ур-ние

Перенесём 1 в правую часть ур-ния

с изменением знака при 1

Получим:
$$\cos{\left(2 x \right)} = -1$$
Это ур-ние преобразуется в
$$2 x = \pi n + \operatorname{acos}{\left(-1 \right)}$$
$$2 x = \pi n - \pi + \operatorname{acos}{\left(-1 \right)}$$
Или
$$2 x = \pi n + \pi$$
$$2 x = \pi n$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$2$$
получим ответ:
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{2}$$
$$x_{2} = \frac{\pi n}{2}$$

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 = -42.4115006098842

x2 = 541.924732890135

x3 = 23.5619451230057

x4 = -26.7035372990183

x5 = -76.9690202568697

x6 = -32.9867227513827

x7 = 17.2787598502655

x8 = -7.85398149857354

x9 = -1.57079642969308

x10 = -70.685834448838

x11 = 10.9955740392793

x12 = 64.4026493086922

x13 = 42.4115007291722

x14 = -10.9955741902138

x15 = 7.85398174058521

x16 = 83.2522052340866

x17 = 32.986722928111

x18 = -92.6769830239371

x19 = 80.1106131434937

x20 = -98.96016883042

x21 = -64.4026491876462

x22 = 86.393797888273

x23 = 80.1106126771746

x24 = -23.5619450090417

x25 = 76.9690200400775

x26 = -73.8274272800405

x27 = 39.2699084246933

x28 = -61.2610569641117

x29 = 23.5619449395428

x30 = -17.2787590276524

x31 = 39.2699081179815

x32 = -54.9778713137198

x33 = 54.9778714849733

x34 = -36.1283154192437

x35 = 20.4203521497111

x36 = -80.1106125795659

x37 = -20.4203520321877

x38 = -89.5353907467661

x39 = 61.2610566752601

x40 = 32.9867226137576

x41 = -76.9690198771149

x42 = -17.2787598091171

x43 = 36.1283156002139

x44 = 58.1194644379895

x45 = 83.2522055730903

x46 = -4.7123889912442

x47 = -98.960168684456

x48 = -95.8185758681287

x49 = -32.9867231091652

x50 = 98.9601683381274

x51 = 51.8362788999928

x52 = 14.1371671048484

x53 = -14.1371668392726

x54 = 70.6858345016621

x55 = -10.9955745350309

x56 = 10.9955743696636

x57 = 17.2787595624179

x58 = 29.845130320338

x59 = -86.393797765473

x60 = -26.7035375427973

x61 = 98.9601685932308

x62 = -48.6946860920117

x63 = -67.5442421675773

x64 = 61.2610569989704

x65 = -92.6769831823972

x66 = 95.8185760590309

x67 = -4.71238872430683

x68 = 73.8274274795554

x69 = -29.8451300963672

x70 = 76.9690207492347

x71 = -70.6858346386357

x72 = -48.6946858738636

x73 = -54.9778716831146

x74 = -58.1194639993376

x75 = -39.2699081528781

x76 = -98.9601684414698

x77 = 92.6769830795146

x78 = 89.5353908552844

x79 = 1.5707965454425

x80 = 48.6946859238715

x81 = 76.9690197631883

x82 = 26.7035373461441

x83 = 67.5442422779275

x84 = 4.71238876848081

x85 = 45.553093700501

x86 = -45.5530935883361

x87 = -51.8362786897497

x88 = -61.2610562242523

x89 = -39.2699083866483

x90 = 54.9778711883962

x91 = -83.2522055415057

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