cos(pi*x/3)=-1 (уравнение)

Найду корень уравнения: cos(pi*x/3)=-1

Вы ввели

   /pi*x\     
cos|----| = -1
   \ 3  /     

$$\cos{\left(\frac{\pi x}{3} \right)} = -1$$

Подробное решение

Дано уравнение
$$\cos{\left(\frac{\pi x}{3} \right)} = -1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$\frac{\pi x}{3} = \pi n + \operatorname{acos}{\left(-1 \right)}$$
$$\frac{\pi x}{3} = \pi n - \pi + \operatorname{acos}{\left(-1 \right)}$$
Или
$$\frac{\pi x}{3} = \pi n + \pi$$
$$\frac{\pi x}{3} = \pi n$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$\frac{\pi}{3}$$
получим ответ:
$$x_{1} = \frac{3 \left(\pi n + \pi\right)}{\pi}$$
$$x_{2} = 3 n$$

Быстрый ответ

x1 = 3

$$x_{1} = 3$$

Сумма и произведение корней

сумма

0 + 3

$$0 + 3$$

=

3

$$3$$

произведение

1*3

$$1 \cdot 3$$

=

3

$$3$$

Численный ответ

x1 = -57.0000003480541

x2 = -33.0000003480541

x3 = -80.9999995602383

x4 = 39.0000002714011

x5 = -2.99999972859885

x6 = -86.9999995602383

x7 = -14.9999995602383

x8 = 9.00000027140115

x9 = 15.0000004397617

x10 = 63.0000004397617

x11 = -81.0000003480541

x12 = -63.0000003480541

x13 = -8.99999972859885

x14 = -56.9999997285989

x15 = -99.0000003480541

x16 = 20.9999996519459

x17 = 111.000000271401

x18 = 68.9999996519459

x19 = 62.9999996519459

x20 = 27.0000002714011

x21 = -39.0000003480541

x22 = 21.0000002714011

x23 = 3.00000027140115

x24 = -62.9999995602383

x25 = 8.99999965194586

x26 = 27.0000004397617

x27 = 75.0000002714011

x28 = 14.9999996519459

x29 = -74.9999997285989

x30 = 63.0000002714011

x31 = 69.0000002714011

x32 = -15.0000003480541

x33 = 80.9999996519459

x34 = 33.0000004397617

x35 = -68.9999997285989

x36 = 87.0000004397617

x37 = 51.0000004397617

x38 = 86.9999996519459

x39 = 69.0000004397617

x40 = -93.0000003480541

x41 = 3.00000043976167

x42 = -20.9999997285989

x43 = -62.9999997285989

x44 = 87.0000002714011

x45 = -14.9999997285989

x46 = 38.9999996519459

x47 = 92.9999996519459

x48 = 51.0000002714011

x49 = 50.9999996519459

x50 = 75.0000004397617

x51 = -50.9999997285989

x52 = 45.0000002714011

x53 = -26.9999997285989

x54 = -26.9999995602383

x55 = 81.0000002714011

x56 = 98.9999996519459

x57 = -20.9999995602383

x58 = -68.9999995602383

x59 = 45.0000004397617

x60 = -74.9999995602383

x61 = 99.0000004397617

x62 = -45.0000003480541

x63 = -27.0000003480541

x64 = -32.9999995602383

x65 = 99.0000002714011

x66 = -3.00000034805414

x67 = -87.0000003480541

x68 = 21.0000004397617

x69 = 57.0000002714011

x70 = 9.00000043976167

x71 = 44.9999996519459

x72 = 33.0000002714011

x73 = 39.0000004397617

x74 = 93.0000004397617

x75 = 74.9999996519459

x76 = 93.0000002714011

x77 = -8.99999956023833

x78 = -92.9999995602383

x79 = -56.9999995602383

x80 = 2.99999965194586

x81 = -38.9999995602383

x82 = -80.9999997285989

x83 = 56.9999996519459

x84 = -44.9999995602383

x85 = 26.9999996519459

x86 = -50.9999995602383

x87 = -38.9999997285989

x88 = -9.00000034805414

x89 = 105.000000271401

x90 = 32.9999996519459

x91 = -98.9999995602383

x92 = -75.0000003480541

x93 = -21.0000003480541

x94 = -2.99999956023833

x95 = 15.0000002714011

x96 = 57.0000004397617

x97 = -32.9999997285989

x98 = 81.0000004397617

x99 = -44.9999997285989

x100 = -51.0000003480541

x101 = -69.0000003480541

График