cos(x/5)=1 (уравнение)

Найду корень уравнения: cos(x/5)=1

Вы ввели

   /x\    
cos|-| = 1
   \5/    

$$\cos{\left(\frac{x}{5} \right)} = 1$$

Подробное решение

Дано уравнение
$$\cos{\left(\frac{x}{5} \right)} = 1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$\frac{x}{5} = \pi n + \operatorname{acos}{\left(1 \right)}$$
$$\frac{x}{5} = \pi n - \pi + \operatorname{acos}{\left(1 \right)}$$
Или
$$\frac{x}{5} = \pi n$$
$$\frac{x}{5} = \pi n - \pi$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$\frac{1}{5}$$
получим ответ:
$$x_{1} = 5 \pi n$$
$$x_{2} = 5 \pi n - 5 \pi$$

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

x2 = 10*pi

$$x_{2} = 10 \pi$$

Сумма и произведение корней

сумма

0 + 0 + 10*pi

$$\left(0 + 0\right) + 10 \pi$$

=

10*pi

$$10 \pi$$

произведение

1*0*10*pi

$$1 \cdot 0 \cdot 10 \pi$$

=

0

$$0$$

Численный ответ

x1 = -31.4159283866218

x2 = 94.2477796093523

x3 = -62.8318517567014

x4 = 62.8318527706332

x5 = 31.41592441948

x6 = -31.4159258271213

x7 = 31.4159241043809

x8 = 94.2477772779978

x9 = -62.8318542822292

x10 = -62.8318555684678

x11 = -1.62235525769729e-6

x12 = 62.8318511342083

x13 = -62.8318551150278

x14 = -31.4159267190991

x15 = 31.4159277493375

x16 = -31.4159239766003

x17 = -94.2477794428473

x18 = -62.831850565019

x19 = -31.4159289358762

x20 = -31.4159276196686

x21 = 31.4159289940735

x22 = -94.2477811632484

x23 = 94.2477770362526

x24 = 2.3450750257112e-6

x25 = -62.8318469155437

x26 = 31.415926864237

x27 = 2.57847256485715e-6

x28 = 62.8318505337848

x29 = 94.2477778692922

x30 = 62.8318555056681

x31 = -94.247782468337

x32 = 31.4159259659256

x33 = 31.4159284938997

x34 = -94.2477770368757

x35 = 94.2477818957824

x36 = 62.8318514503512

x37 = -31.4159262477149

x38 = 94.2477804655271

x39 = 6.57859066527638e-7

x40 = 31.4159281552551

x41 = -5.7404755663588e-6

x42 = 31.4159215452388

x43 = 0.0

x44 = 62.8318536690684

x45 = 62.8318538766212

x46 = -2.56821576818567e-6

x47 = -94.2477803289257

x48 = -62.8318543978453

x49 = 62.8318556092102

x50 = -94.2477818166386

x51 = -94.2477785355385

x52 = 9.65843137539203e-7

x53 = 94.2477812789845

x54 = -62.8318510360733

x55 = 31.415929078517

x56 = -62.8318517428508

x57 = 1.76056362043436e-6

x58 = 62.8318552066789

x59 = -62.8318535287702

x60 = 62.8318580491983

x61 = 62.8318506266524

x62 = -94.2477772108419

x63 = -8.31066507151233e-7

x64 = -62.8318526281476

x65 = -1.64845150845946e-6

x66 = -31.4159231706356

x67 = 31.4159240090655

x68 = 2.08786336067684e-6

x69 = -31.4159241769778

x70 = 879.645937560211

x71 = 94.2477786682919

x72 = -314.159267572554

x73 = -31.4159249905105

x74 = 94.2477775194291

x75 = -2.22118925947804e-6

x76 = -94.2477776882079

x77 = -31.4159243329344

x78 = 534.070752556753

x79 = -62.8318555589901

x80 = -94.2477777610472

x81 = 62.8318518838389

x82 = -31.4159290957676

x83 = -31.4159283913017

x84 = 94.247785326877

x85 = 94.2477812203521

x86 = -62.8318505755408

x87 = -62.8318593692532

x88 = -2.27175563036052e-6

x89 = 62.8318545211865

x90 = 31.4159257270151

x91 = 31.4159251107842

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