sin((pi*x)/4)=-1 (уравнение)

Найду корень уравнения: sin((pi*x)/4)=-1

Вы ввели

   /pi*x\     
sin|----| = -1
   \ 4  /     

$$\sin{\left (\frac{\pi x}{4} \right )} = -1$$

Подробное решение

Дано уравнение
$$\sin{\left (\frac{\pi x}{4} \right )} = -1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$\frac{\pi x}{4} = 2 \pi n + \operatorname{asin}{\left (-1 \right )}$$
$$\frac{\pi x}{4} = 2 \pi n - \operatorname{asin}{\left (-1 \right )} + \pi$$
Или
$$\frac{\pi x}{4} = 2 \pi n - \frac{\pi}{2}$$
$$\frac{\pi x}{4} = 2 \pi n + \frac{3 \pi}{2}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$\frac{\pi}{4}$$
получим ответ:
$$x_{1} = \frac{1}{\pi} \left(8 \pi n - 2 \pi\right)$$
$$x_{2} = \frac{1}{\pi} \left(8 \pi n + 6 \pi\right)$$

Быстрый ответ

x1 = -2

$$x_{1} = -2$$

x2 = 6

$$x_{2} = 6$$

Численный ответ

x1 = -33.9999993441000

x2 = -50.0000006396000

x3 = 94.0000000000000

x4 = 78.0000000000000

x5 = 6.00000000000000

x6 = 54.0000000000000

x7 = -34.0000006396000

x8 = 70.0000006559000

x9 = -90.0000006396000

x10 = -1.99999934408000

x11 = -97.9999993441000

x12 = 22.0000006559000

x13 = -26.0000006396000

x14 = -50.0000000000000

x15 = -74.0000006396000

x16 = -2.00000000000000

x17 = 54.0000006559000

x18 = -98.0000006396000

x19 = -25.9999993441000

x20 = 70.0000000000000

x21 = -82.0000000000000

x22 = -18.0000006396000

x23 = -26.0000000000000

x24 = -90.0000000000000

x25 = -74.0000000000000

x26 = 13.9999993604000

x27 = 45.9999993604000

x28 = 46.0000000000000

x29 = -58.0000006396000

x30 = 46.0000006559000

x31 = 30.0000006559000

x32 = -34.0000000000000

x33 = -65.9999993441000

x34 = 69.9999993604000

x35 = 38.0000000000000

x36 = -81.9999993441000

x37 = -66.0000000000000

x38 = -10.0000000000000

x39 = 77.9999993604000

x40 = 37.9999993604000

x41 = -42.0000000000000

x42 = -42.0000006396000

x43 = -66.0000006396000

x44 = -57.9999993441000

x45 = 62.0000000000000

x46 = -73.9999993441000

x47 = 29.9999993604000

x48 = 62.0000006559000

x49 = -2.00000063964000

x50 = 22.0000000000000

x51 = 101.999999360000

x52 = -17.9999993441000

x53 = 5.99999936036000

x54 = 38.0000006559000

x55 = -41.9999993441000

x56 = 78.0000006559000

x57 = -9.99999934408000

x58 = 94.0000006559000

x59 = 53.9999993604000

x60 = 14.0000006559000

x61 = 93.9999993604000

x62 = 30.0000000000000

x63 = -89.9999993441000

x64 = 14.0000000000000

x65 = 85.9999993604000

x66 = 86.0000000000000

x67 = -58.0000000000000

x68 = 6.00000065592000

x69 = -98.0000000000000

x70 = -49.9999993441000

x71 = 61.9999993604000

x72 = -10.0000006396000

x73 = 86.0000006559000

x74 = -18.0000000000000

x75 = 21.9999993604000

x76 = -82.0000006396000