|cos(x)|=1 (уравнение)

Найду корень уравнения: |cos(x)|=1

Вы ввели

|cos(x)| = 1

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

Подробное решение

Дано уравнение
$$\left|{\cos{\left(x \right)}}\right| = 1$$
преобразуем
$$\left|{\cos{\left(x \right)}}\right| - 1 = 0$$
$$\left|{\cos{\left(x \right)}}\right| - 1 = 0$$
Сделаем замену
$$w = \left|{\cos{\left(x \right)}}\right|$$
Переносим свободные слагаемые (без w)
из левой части в правую, получим:
$$w = 1$$
Получим ответ: w = 1
делаем обратную замену
$$\left|{\cos{\left(x \right)}}\right| = w$$
подставляем w:

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

x2 = pi

$$x_{2} = \pi$$

x3 = 2*pi

$$x_{3} = 2 \pi$$

Сумма и произведение корней

сумма

0 + 0 + pi + 2*pi

$$\left(\left(0 + 0\right) + \pi\right) + 2 \pi$$

=

3*pi

$$3 \pi$$

произведение

1*0*pi*2*pi

$$2 \pi 1 \cdot 0 \pi$$

=

0

$$0$$

Численный ответ

x1 = 25.1327416384075

x2 = 12.5663704426592

x3 = 40.8407042062167

x4 = 97.389372581711

x5 = 40.8407049800347

x6 = -81.6814090382277

x7 = 75.3982232188727

x8 = -84.8230012511693

x9 = -3.14159295109225

x10 = 65.9734457529812

x11 = 47.123889410773

x12 = 97.3893717959212

x13 = 28.2743338651796

x14 = 81.6814091897036

x15 = -18.8495555173448

x16 = -6.2831851275477

x17 = -56.5486682426592

x18 = -37.6991128371258

x19 = 50.2654824463392

x20 = -62.8318534787248

x21 = -25.1327407505866

x22 = 100.530964759815

x23 = 31.4159268459961

x24 = -87.9645943586158

x25 = -12.5663710889626

x26 = 62.8318527849002

x27 = 37.6991120311338

x28 = 91.1061865667532

x29 = -69.1150386869085

x30 = -3.14159217367683

x31 = 69.115038794053

x32 = 53.4070746418597

x33 = -28.2743337069329

x34 = -9.4247781365785

x35 = -50.2654822863493

x36 = -47.1238901083229

x37 = -91.1061864815274

x38 = -43.9822971745392

x39 = -84.8230020565447

x40 = 87.964594335905

x41 = 56.5486676011951

x42 = 75.3982240031607

x43 = 31.4159260648825

x44 = 72.2566310277176

x45 = -12.5663703112531

x46 = -56.5486674685864

x47 = -21.9911485864417

x48 = -75.3982238741744

x49 = 87.9645942336512

x50 = 18.8495564031971

x51 = -40.8407040952604

x52 = -94.2477794452815

x53 = -40.8407049008781

x54 = -18.8495563230046

x55 = -97.3893729145565

x56 = -75.3982221405918

x57 = -100.530964626003

x58 = -91.106187265474

x59 = -97.3893724533348

x60 = -72.2566308657983

x61 = 62.8318535568358

x62 = -78.5398168194507

x63 = -31.4159267157965

x64 = 9.42477826738203

x65 = 25.1327408328211

x66 = 18.8495556275525

x67 = 3.14159306054457

x68 = 15.7079634518075

x69 = -53.407075294995

x70 = 91.1061873718352

x71 = -34.5575196658297

x72 = -25.1327415297174

x73 = -12.5663705813442

x74 = 94.2477796093523

x75 = 43.9822971694647

x76 = -15.7079632965989

x77 = -37.6991118772631

x78 = 34.5575190219169

x79 = 21.9911485852059

x80 = -65.9734457649277

x81 = 0.0

x82 = 9.42477748794163

x83 = 78.5398161804942

x84 = 84.8230013636028

x85 = 84.8230021335997

x86 = -78.5398160472843

x87 = -47.1238893275319

x88 = 3.14159211708139

x89 = 59.6902606104322

x90 = -12.5663715061514

x91 = 69.1150379887504

x92 = -81.6814093609983

x93 = 53.407075424589

x94 = 3.1415922548952

x95 = -69.1150379045123

x96 = -62.831852673202

x97 = -59.6902604578012

x98 = 47.1238902162437

x99 = 6.28318528420851

x100 = -34.5575188899093

График