cos(pi+x)=1 (уравнение)

Найду корень уравнения: cos(pi+x)=1

Вы ввели

cos(pi + x) = 1

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

Подробное решение

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

Разделим обе части ур-ния на -1

Ур-ние превратится в
$$\cos{\left(x \right)} = -1$$
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(-1 \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(-1 \right)}$$
Или
$$x = \pi n + \pi$$
$$x = \pi n$$
, где n - любое целое число

Быстрый ответ

x1 = pi

$$x_{1} = \pi$$

Сумма и произведение корней

сумма

0 + pi

$$0 + \pi$$

=

pi

$$\pi$$

произведение

1*pi

$$1 \pi$$

=

pi

$$\pi$$

Численный ответ

x1 = -15.7079635641079

x2 = 72.2566310277176

x3 = 91.1061865667532

x4 = -65.9734461969855

x5 = 97.389372581711

x6 = -40.8407040952604

x7 = 15.7079634518075

x8 = 40.8407045848602

x9 = 65.9734452390837

x10 = -34.5575188899093

x11 = -72.2566308657983

x12 = 59.6902600526626

x13 = 53.407075424589

x14 = 53.4070766553897

x15 = -78.5398160472843

x16 = 15.7079627593774

x17 = 40.8407049800347

x18 = 40.8407045792514

x19 = -97.3893716284562

x20 = -15.707962774825

x21 = -59.6902606928653

x22 = 9.42477748794163

x23 = 59.6902599104079

x24 = -97.3893724533348

x25 = 21.9911485852059

x26 = 65.9734457529812

x27 = -53.407075294995

x28 = 3.14159306054457

x29 = 59.6902606104322

x30 = 15.707963957033

x31 = 21.9911489072506

x32 = 28.2743338651796

x33 = -21.9911490521325

x34 = 91.1061873718352

x35 = -34.5575196658297

x36 = 40.8407042062167

x37 = 97.3893717959212

x38 = -91.1061864815274

x39 = 84.8230021335997

x40 = -9.4247781365785

x41 = -47.1238893275319

x42 = 78.5398161804942

x43 = -47.1238901083229

x44 = -3.14159217367683

x45 = 3.1415922548952

x46 = -9.42477752082051

x47 = -59.6902604578012

x48 = -40.8407049290801

x49 = -53.4070745786761

x50 = -28.2743337069329

x51 = -53.4070745963886

x52 = -78.5398168194507

x53 = 78.5398149750205

x54 = -21.9911485864417

x55 = -65.9734457649277

x56 = 28.2743335663982

x57 = -28.2743340989896

x58 = -3.14159295109225

x59 = -9.42477744529557

x60 = 78.5398168562347

x61 = 47.1238902162437

x62 = -84.8230012511693

x63 = 53.4070746418597

x64 = -91.106187265474

x65 = 72.2566306985

x66 = 78.5398152766482

x67 = 28.2743343711514

x68 = 9.42477826738203

x69 = 78.5398166181283

x70 = -40.8407049008781

x71 = 34.5575197055812

x72 = 65.9734460390947

x73 = -15.7079632965989

x74 = -1127.83176318906

x75 = 34.5575190219169

x76 = 15.7079629803241

x77 = 34.5575195449229

x78 = -28.2743343914215

x79 = -65.9734453607004

x80 = -84.8230020565447

x81 = -72.2566315419804

x82 = 47.123889410773

x83 = -59.6902599212271

x84 = -97.3893717476911

x85 = -72.2566311847166

x86 = -65.9734449870253

x87 = 84.8230013636028

x88 = 72.2566315166773

x89 = -21.991148226056

x90 = 21.9911480932338

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