sin(2π*x)=-1 (уравнение)

Найду корень уравнения: sin(2π*x)=-1

Вы ввели

sin(2*pi*x) = -1

$$\sin{\left(2 \pi x \right)} = -1$$

Подробное решение

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

Быстрый ответ

x1 = -1/4

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

x2 = 3/4

$$x_{2} = \frac{3}{4}$$

Сумма и произведение корней

сумма

0 - 1/4 + 3/4

$$\left(- \frac{1}{4} + 0\right) + \frac{3}{4}$$

=

1/2

$$\frac{1}{2}$$

произведение

1*-1/4*3/4

$$1 \left(- \frac{1}{4}\right) \frac{3}{4}$$

=

-3/16

$$- \frac{3}{16}$$

Численный ответ

x1 = 61.75

x2 = 25.75

x3 = 21.75

x4 = 51.75

x5 = 55.75

x6 = -94.25

x7 = -98.25

x8 = -100.25

x9 = -90.25

x10 = -78.25

x11 = -0.25

x12 = 27.75

x13 = -68.25

x14 = -76.25

x15 = -48.25

x16 = 9.75

x17 = 81.75

x18 = 87.75

x19 = 69.75

x20 = -10.25

x21 = -54.25

x22 = 95.75

x23 = -38.25

x24 = -42.25

x25 = -44.25

x26 = -2.25

x27 = -80.25

x28 = 41.75

x29 = 91.75

x30 = -22.25

x31 = -20.25

x32 = -58.25

x33 = -60.25

x34 = -56.25

x35 = -84.25

x36 = 99.75

x37 = -14.25

x38 = 11.75

x39 = 39.75

x40 = 65.75

x41 = -34.25

x42 = -50.25

x43 = 13.75

x44 = 63.75

x45 = 89.75

x46 = 83.75

x47 = 49.75

x48 = -88.25

x49 = 53.75

x50 = -70.25

x51 = -72.25

x52 = 77.75

x53 = 45.75

x54 = -96.25

x55 = -82.25

x56 = -52.25

x57 = -62.25

x58 = 31.75

x59 = 67.75

x60 = 17.75

x61 = -28.25

x62 = 19.75

x63 = -32.25

x64 = -16.25

x65 = 57.75

x66 = -4.25

x67 = 15.75

x68 = 85.75

x69 = 3.75

x70 = -46.25

x71 = -8.25

x72 = 75.75

x73 = 79.75

x74 = 59.75

x75 = 73.75

x76 = -36.25

x77 = -26.25

x78 = 93.75

x79 = -30.25

x80 = -6.25

x81 = 35.75

x82 = -18.25

x83 = 97.75

x84 = 37.75

x85 = -64.25

x86 = -86.25

x87 = 43.75

x88 = 71.75

x89 = 7.75

x90 = -92.25

x91 = -40.25

x92 = 29.75

x93 = 5.75

x94 = 23.75

x95 = 1.75

x96 = -24.25

x97 = 33.75

x98 = 47.75

x99 = -12.25

x100 = -74.25

x101 = -66.25

График