cos(x/9)=-1 (уравнение)

Найду корень уравнения: cos(x/9)=-1

Вы ввели

   /x\     
cos|-| = -1
   \9/     

$$\cos{\left(\frac{x}{9} \right)} = -1$$

Подробное решение

Дано уравнение
$$\cos{\left(\frac{x}{9} \right)} = -1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$\frac{x}{9} = \pi n + \operatorname{acos}{\left(-1 \right)}$$
$$\frac{x}{9} = \pi n - \pi + \operatorname{acos}{\left(-1 \right)}$$
Или
$$\frac{x}{9} = \pi n + \pi$$
$$\frac{x}{9} = \pi n$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$\frac{1}{9}$$
получим ответ:
$$x_{1} = 9 \pi n + 9 \pi$$
$$x_{2} = 9 \pi n$$

Быстрый ответ

x1 = 9*pi

$$x_{1} = 9 \pi$$

Сумма и произведение корней

сумма

0 + 9*pi

$$0 + 9 \pi$$

=

9*pi

$$9 \pi$$

произведение

1*9*pi

$$1 \cdot 9 \pi$$

=

9*pi

$$9 \pi$$

Численный ответ

x1 = -84.8229984183414

x2 = -28.2743244393303

x3 = 84.8230062578477

x4 = 28.2743294622997

x5 = -28.274336330782

x6 = 84.8229975208727

x7 = -84.8230038722992

x8 = -28.2743302346196

x9 = 84.8230047653464

x10 = 84.8230013495227

x11 = 84.8229980777778

x12 = -28.2743364292376

x13 = 28.2743304915216

x14 = 84.8230022514225

x15 = -28.2743327790057

x16 = 28.2743364538745

x17 = -84.8230021094102

x18 = -28.274339777417

x19 = 28.2743321226647

x20 = 84.8230031513295

x21 = -28.2743337037926

x22 = -28.2743377221286

x23 = 28.2743312171058

x24 = -28.2743379604922

x25 = 28.2743293800044

x26 = -28.2743384786006

x27 = 84.8230094379697

x28 = -84.8230046531045

x29 = 84.8230133302236

x30 = -28.2743298129891

x31 = 84.8230059222781

x32 = -84.8230012061093

x33 = 28.2743292565571

x34 = -28.2743294244728

x35 = -28.2743345970395

x36 = 84.8230054187347

x37 = -84.8229971027767

x38 = 28.2743356255459

x39 = -84.8229986568907

x40 = 28.2743382637136

x41 = -84.8230062672539

x42 = 84.8229972620779

x43 = 28.2743329181609

x44 = 28.2743347376362

x45 = -28.2743370851987

x46 = 28.2743338651726

x47 = -28.2743354915365

x48 = 350403.819800956

x49 = -28.2743292434126

x50 = -28.2743319046916

x51 = 28.2743383693941

x52 = -28.2743318847664

x53 = 28.2743320361609

x54 = 28.2743371926722

x55 = 28.27433780891

x56 = -28.2743310978195

x57 = 84.823015508603

x58 = 84.8230004361691

x59 = 84.8229987720126

x60 = -84.82300619224

x61 = -84.82300585417

x62 = -28.2743384609725

x63 = 84.8230039988447

x64 = -84.8230015620127

x65 = -84.8229970158338

x66 = -28.274338203618

x67 = -28.2743303891955

x68 = 84.8230062279496

x69 = -84.8229974478895

x70 = -84.8229994399868

x71 = 84.8229995685748

x72 = 84.8229970158031

x73 = -28.2743294108294

x74 = -84.8230067803298

x75 = -84.82301110703

x76 = -84.8230030151146

x77 = -84.8229973288789

x78 = 84.8229971449237

x79 = 28.2743385035735

x80 = 28.2743360993878

x81 = 84.8230009536101

x82 = -28.274332567917

x83 = 28.274338435343

x84 = 28.2743308477367

x85 = 28.2743378457644

x86 = -84.8230053257351

x87 = -84.8229979809901

x88 = 84.822998213206

x89 = -84.8230002987033

x90 = 28.2743298931087

x91 = 28.2743300805649

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