cos(pix)=1 (уравнение)

Найду корень уравнения: cos(pix)=1

Вы ввели

cos(pi*x) = 1

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

Подробное решение

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

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

x2 = 2

$$x_{2} = 2$$

Сумма и произведение корней

сумма

2

$$2$$

=

2

$$2$$

произведение

0*2

$$0 \cdot 2$$

=

0

$$0$$

Численный ответ

x1 = -24.0

x2 = 94.0

x3 = -64.0

x4 = 58.0

x5 = -22.0

x6 = 16.0

x7 = -80.0

x8 = -42.0

x9 = -12.0

x10 = -28.0

x11 = -16.0

x12 = 98.0

x13 = -70.0

x14 = -60.0

x15 = -54.0

x16 = 28.0

x17 = 38.0

x18 = -38.0

x19 = -94.0

x20 = -74.0

x21 = -52.0

x22 = -84.0

x23 = 80.0

x24 = 96.0

x25 = -90.0

x26 = -78.0

x27 = 68.0

x28 = 66.0

x29 = 52.0

x30 = -30.0

x31 = -62.0

x32 = 0.0

x33 = -96.0

x34 = -48.0

x35 = -44.0

x36 = 76.0

x37 = 10.0

x38 = -2.0

x39 = -82.0

x40 = 78.0

x41 = -58.0

x42 = 92.0

x43 = 18.0

x44 = 46.0

x45 = 2.0

x46 = -76.0

x47 = -8.0

x48 = 84.0

x49 = 62.0

x50 = 48.0

x51 = 40.0

x52 = 14.0

x53 = -88.0

x54 = 24.0

x55 = 34.0

x56 = 100.0

x57 = 32.0

x58 = -4.0

x59 = -40.0

x60 = -20.0

x61 = 42.0

x62 = 88.0

x63 = -32.0

x64 = 8.0

x65 = -26.0

x66 = 6.0

x67 = 64.0

x68 = -68.0

x69 = 72.0

x70 = 70.0

x71 = -10.0

x72 = 50.0

x73 = -50.0

x74 = -18.0

x75 = 30.0

x76 = 54.0

x77 = -98.0

x78 = -6.0

x79 = -46.0

x80 = 44.0

x81 = 20.0

x82 = 86.0

x83 = -92.0

x84 = -72.0

x85 = 12.0

x86 = -36.0

x87 = 74.0

x88 = 56.0

x89 = -86.0

x90 = 26.0

x91 = 82.0

x92 = -66.0

x93 = 90.0

x94 = 22.0

x95 = 60.0

x96 = -34.0

x97 = -56.0

x98 = 4.0

x99 = 36.0

x100 = -100.0

x101 = -14.0

График