cot(pi*x)=1 (уравнение)

Найду корень уравнения: cot(pi*x)=1

Вы ввели

cot(pi*x) = 1

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

Подробное решение

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

Быстрый ответ

x1 = 1/4

$$x_{1} = \frac{1}{4}$$

Сумма и произведение корней

сумма

0 + 1/4

$$0 + \frac{1}{4}$$

=

1/4

$$\frac{1}{4}$$

произведение

1*1/4

$$1 \cdot \frac{1}{4}$$

=

1/4

$$\frac{1}{4}$$

Численный ответ

x1 = 14.25

x2 = 28.25

x3 = -33.75

x4 = -61.75

x5 = -91.75

x6 = -83.75

x7 = 56.25

x8 = -37.75

x9 = -67.75

x10 = -1.75

x11 = 76.25

x12 = 88.25

x13 = -79.75

x14 = -15.75

x15 = -31.75

x16 = -55.75

x17 = 86.25

x18 = 6.25

x19 = -47.75

x20 = 84.25

x21 = 72.25

x22 = 64.25

x23 = 26.25

x24 = -63.75

x25 = -45.75

x26 = -99.75

x27 = -85.75

x28 = 20.25

x29 = 38.25

x30 = -77.75

x31 = 54.25

x32 = -27.75

x33 = 70.25

x34 = 96.25

x35 = 62.25

x36 = -89.75

x37 = -5.75

x38 = -81.75

x39 = -49.75

x40 = -35.75

x41 = 12.25

x42 = -87.75

x43 = 78.25

x44 = -65.75

x45 = -59.75

x46 = 40.25

x47 = 68.25

x48 = -69.75

x49 = 4.25

x50 = 48.25

x51 = 66.25

x52 = -43.75

x53 = 92.25

x54 = 80.25

x55 = -25.75

x56 = -23.75

x57 = -21.75

x58 = 46.25

x59 = -71.75

x60 = -39.75

x61 = 34.25

x62 = 18.25

x63 = 16.25

x64 = 10.25

x65 = -75.75

x66 = -51.75

x67 = -97.75

x68 = 44.25

x69 = -29.75

x70 = 90.25

x71 = -93.75

x72 = 98.25

x73 = 32.25

x74 = -3.75

x75 = 100.25

x76 = 36.25

x77 = 58.25

x78 = -17.75

x79 = 30.25

x80 = 94.25

x81 = 82.25

x82 = -7.75

x83 = -9.75

x84 = 42.25

x85 = 50.25

x86 = -11.75

x87 = -95.75

x88 = -13.75

x89 = -57.75

x90 = 2.25

x91 = 22.25

x92 = 60.25

x93 = 24.25

x94 = -19.75

x95 = 52.25

x96 = 74.25

x97 = -73.75

x98 = 8.25

x99 = -53.75

x100 = -41.75

График