cos(x/4)=-1 (уравнение)

Найду корень уравнения: cos(x/4)=-1

Вы ввели

   /x\     
cos|-| = -1
   \4/     

$$\cos{\left(\frac{x}{4} \right)} = -1$$

Подробное решение

Дано уравнение
$$\cos{\left(\frac{x}{4} \right)} = -1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$\frac{x}{4} = \pi n + \operatorname{acos}{\left(-1 \right)}$$
$$\frac{x}{4} = \pi n - \pi + \operatorname{acos}{\left(-1 \right)}$$
Или
$$\frac{x}{4} = \pi n + \pi$$
$$\frac{x}{4} = \pi n$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$\frac{1}{4}$$
получим ответ:
$$x_{1} = 4 \pi n + 4 \pi$$
$$x_{2} = 4 \pi n$$

Быстрый ответ

x1 = 4*pi

$$x_{1} = 4 \pi$$

Сумма и произведение корней

сумма

0 + 4*pi

$$0 + 4 \pi$$

=

4*pi

$$4 \pi$$

произведение

1*4*pi

$$1 \cdot 4 \pi$$

=

4*pi

$$4 \pi$$

Численный ответ

x1 = 62.8318536665011

x2 = 62.8318519341968

x3 = 37.6991126313527

x4 = 62.8318512546705

x5 = -62.8318526291934

x6 = 87.9645943359506

x7 = -62.8318535276195

x8 = 37.6991098556079

x9 = 87.9645933013076

x10 = 62.831855052783

x11 = -62.8318543665598

x12 = 816.814092941514

x13 = 37.6991136049128

x14 = 12.5663725259384

x15 = -37.6991110157527

x16 = -12.566372588574

x17 = -87.9645977722203

x18 = 150080.164244827

x19 = 87.9645959885307

x20 = 87.9645924960813

x21 = -12.5663694311055

x22 = -12.5663711900163

x23 = -37.6991127942856

x24 = 87.9645903543651

x25 = 37.699112921042

x26 = 87.9645962702062

x27 = 12.566375490852

x28 = -37.6991098134356

x29 = 87.9645922795914

x30 = 12.5663688653578

x31 = 12.5663685581022

x32 = 37.6991099388154

x33 = 87.9645952698126

x34 = -314.159265522087

x35 = 12.5663713265724

x36 = 62.8318550266814

x37 = 37.6991068639949

x38 = 12.5663695540465

x39 = -87.9645926332176

x40 = 12.5663698830334

x41 = -37.6991118772975

x42 = 37.6991120348055

x43 = -87.9645943585672

x44 = 87.9645963565927

x45 = -37.6991100302327

x46 = 62.8318519057004

x47 = -62.8318522922141

x48 = -62.8318550919992

x49 = -37.6991134646708

x50 = -62.8318517869837

x51 = 37.6991132740765

x52 = -37.6991138912933

x53 = -37.6991077917585

x54 = 37.6991103590388

x55 = 12.5663726112938

x56 = 12.5663704398551

x57 = 12.5663691974864

x58 = -87.9645926239255

x59 = 37.6991139066307

x60 = -12.5663706565795

x61 = -12.5663725589991

x62 = -87.9645922485051

x63 = -87.9645963286501

x64 = -12.566370294752

x65 = 87.9645959330169

x66 = -12.5663685569103

x67 = 62.8318527709646

x68 = 87.964592729056

x69 = -12.5663694578299

x70 = -87.964593360727

x71 = -87.9645958943999

x72 = -62.831853699831

x73 = -87.9645951396381

x74 = -12.5663687851827

x75 = -62.8318511822964

x76 = 37.6991111497125

x77 = -37.6991102571018

x78 = 62.8318510212199

x79 = -37.6991137320904

x80 = -37.6991135174989

x81 = -87.964591943009

x82 = -87.9645960722761

x83 = 12.5663721136039

x84 = 62.8318544793224

x85 = 87.9645934917479

x86 = 62.8318531539994

x87 = -12.566372006031

x88 = -62.8318549650823

x89 = -62.8318510361526

График