tg(pi*x)=1 (уравнение)

Найду корень уравнения: tg(pi*x)=1

Вы ввели

tan(pi*x) = 1

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

Подробное решение

Дано уравнение
$$\tan{\left(\pi x \right)} = 1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$\pi x = \pi n + \operatorname{atan}{\left(1 \right)}$$
Или
$$\pi x = \pi n + \frac{\pi}{4}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$\pi$$
получим ответ:
$$x_{1} = \frac{\pi n + \frac{\pi}{4}}{\pi}$$

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 = 36.25

x2 = 18.25

x3 = -19.75

x4 = 74.25

x5 = 100.25

x6 = 94.25

x7 = -15.75

x8 = 96.25

x9 = 90.25

x10 = 68.25

x11 = -99.75

x12 = -17.75

x13 = -25.75

x14 = 38.25

x15 = 32.25

x16 = 8.25

x17 = 46.25

x18 = -69.75

x19 = 52.25

x20 = 72.25

x21 = 76.25

x22 = 80.25

x23 = -53.75

x24 = 56.25

x25 = 44.25

x26 = 16.25

x27 = 24.25

x28 = 26.25

x29 = -71.75

x30 = 54.25

x31 = -37.75

x32 = -59.75

x33 = -49.75

x34 = 48.25

x35 = 82.25

x36 = -5.75

x37 = -13.75

x38 = -83.75

x39 = -31.75

x40 = -9.75

x41 = -91.75

x42 = 66.25

x43 = 28.25

x44 = 14.25

x45 = 6.25

x46 = -41.75

x47 = -39.75

x48 = 20.25

x49 = -11.75

x50 = 88.25

x51 = -23.75

x52 = -51.75

x53 = -35.75

x54 = -1.75

x55 = -47.75

x56 = -93.75

x57 = -33.75

x58 = 30.25

x59 = -27.75

x60 = -21.75

x61 = 62.25

x62 = -63.75

x63 = 64.25

x64 = -81.75

x65 = 50.25

x66 = -95.75

x67 = 12.25

x68 = 60.25

x69 = 40.25

x70 = -97.75

x71 = 34.25

x72 = -45.75

x73 = 4.25

x74 = -85.75

x75 = 84.25

x76 = -65.75

x77 = -3.75

x78 = 58.25

x79 = -89.75

x80 = 98.25

x81 = 92.25

x82 = -43.75

x83 = 78.25

x84 = -73.75

x85 = -7.75

x86 = -75.75

x87 = 10.25

x88 = -79.75

x89 = 0.25

x90 = -77.75

x91 = 86.25

x92 = -57.75

x93 = 22.25

x94 = 70.25

x95 = -67.75

x96 = -61.75

x97 = -29.75

x98 = -55.75

x99 = -87.75

x100 = 42.25

x101 = 2.25

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