sin((pi*x)/4)=-1 (уравнение)

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

    Решение

    Вы ввели
    [LaTeX]
       /pi*x\     
    sin|----| = -1
       \ 4  /     
    $$\sin{\left (\frac{\pi x}{4} \right )} = -1$$
    Подробное решение
    [LaTeX]
    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:
    $$x_{1} = \frac{1}{\pi} \left(8 \pi n - 2 \pi\right)$$
    $$x_{2} = \frac{1}{\pi} \left(8 \pi n + 6 \pi\right)$$
    График
    [LaTeX]
    Быстрый ответ
    [LaTeX]
    x1 = -2
    $$x_{1} = -2$$
    x2 = 6
    $$x_{2} = 6$$
    Численный ответ
    [LaTeX]
    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