sin(2pi*x)=1 (уравнение)

Найду корень уравнения: sin(2pi*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
$$2 \pi x = 2 \pi n + \frac{\pi}{2}$$
$$2 \pi x = 2 \pi n + \frac{\pi}{2}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$2 \pi$$
получим ответ:
$$x_{1} = \frac{2 \pi n + \frac{\pi}{2}}{2 \pi}$$
$$x_{2} = \frac{2 \pi n + \frac{\pi}{2}}{2 \pi}$$

Быстрый ответ

x1 = 1/4

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

Сумма и произведение корней

сумма

1/4

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

=

1/4

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

произведение

1/4

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

=

1/4

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

Численный ответ

x1 = -75.75

x2 = 94.25

x3 = -39.75

x4 = 22.25

x5 = -91.75

x6 = -49.75

x7 = -73.75

x8 = 92.25

x9 = -31.75

x10 = -45.75

x11 = 68.25

x12 = -3.75

x13 = 78.25

x14 = -95.75

x15 = 60.25

x16 = -59.75

x17 = -55.75

x18 = 100.25

x19 = 46.25

x20 = 56.25

x21 = 72.25

x22 = -89.75

x23 = -79.75

x24 = 42.25

x25 = -65.75

x26 = 66.25

x27 = -47.75

x28 = 32.25

x29 = 44.25

x30 = -29.75

x31 = 6.25

x32 = -61.75

x33 = -7.75

x34 = 48.25

x35 = 26.25

x36 = -21.75

x37 = 84.25

x38 = -87.75

x39 = 8.25

x40 = 98.25

x41 = 74.25

x42 = -53.75

x43 = -9.75

x44 = -23.75

x45 = -71.75

x46 = 28.25

x47 = -15.75

x48 = 96.25

x49 = -83.75

x50 = 40.25

x51 = 14.25

x52 = -99.75

x53 = 88.25

x54 = -77.75

x55 = -17.75

x56 = -63.75

x57 = 80.25

x58 = 54.25

x59 = -57.75

x60 = -67.75

x61 = -27.75

x62 = -85.75

x63 = -1.75

x64 = 38.25

x65 = 12.25

x66 = 24.25

x67 = -97.75

x68 = 90.25

x69 = -51.75

x70 = -43.75

x71 = 64.25

x72 = -11.75

x73 = 58.25

x74 = 76.25

x75 = 82.25

x76 = 86.25

x77 = 30.25

x78 = 20.25

x79 = 10.25

x80 = 0.25

x81 = -25.75

x82 = 52.25

x83 = -33.75

x84 = 34.25

x85 = -81.75

x86 = -5.75

x87 = 18.25

x88 = -69.75

x89 = 4.25

x90 = -19.75

x91 = -13.75

x92 = 62.25

x93 = 50.25

x94 = -41.75

x95 = 16.25

x96 = 36.25

x97 = 2.25

x98 = -37.75

x99 = -35.75

x100 = 70.25

x101 = -93.75

График