cos(pi*x/3)=-1/2 (уравнение)

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    Найду корень уравнения: cos(pi*x/3)=-1/2

    Решение

    Вы ввели
    [LaTeX]
       /pi*x\       
    cos|----| = -1/2
       \ 3  /       
    $$\cos{\left (\frac{\pi x}{3} \right )} = - \frac{1}{2}$$
    Подробное решение
    [LaTeX]
    Дано уравнение
    $$\cos{\left (\frac{\pi x}{3} \right )} = - \frac{1}{2}$$
    - это простейшее тригонометрическое ур-ние
    Это ур-ние преобразуется в
    $$\frac{\pi x}{3} = \pi n + \operatorname{acos}{\left (- \frac{1}{2} \right )}$$
    $$\frac{\pi x}{3} = \pi n - \pi + \operatorname{acos}{\left (- \frac{1}{2} \right )}$$
    Или
    $$\frac{\pi x}{3} = \pi n + \frac{2 \pi}{3}$$
    $$\frac{\pi x}{3} = \pi n - \frac{\pi}{3}$$
    , где n - любое целое число
    Разделим обе части полученного ур-ния на
    $$\frac{\pi}{3}$$
    получим ответ:
    $$x_{1} = \frac{1}{\pi} \left(3 \pi n + 2 \pi\right)$$
    $$x_{2} = \frac{1}{\pi} \left(3 \pi n - \pi\right)$$
    График
    [LaTeX]
    Быстрый ответ
    [LaTeX]
    x1 = 2
    $$x_{1} = 2$$
    x2 = 4
    $$x_{2} = 4$$
    Численный ответ
    [LaTeX]
    x1 = -32.0000000000000
    x2 = 542.000000000000
    x3 = 94.0000000000000
    x4 = 52.0000000000000
    x5 = 520.000000000000
    x6 = 32.0000000000000
    x7 = 92.0000000000000
    x8 = -100.000000000000
    x9 = 556.000000000000
    x10 = 1546.00000000000
    x11 = 16.0000000000000
    x12 = -46.0000000000000
    x13 = -50.0000000000000
    x14 = -88.0000000000000
    x15 = 80.0000000000000
    x16 = 760.000000000000
    x17 = 4.00000000000000
    x18 = 34.0000000000000
    x19 = 2.00000000000000
    x20 = 70.0000000000000
    x21 = -82.0000000000000
    x22 = 584.000000000000
    x23 = -58.0000000000000
    x24 = -28.0000000000000
    x25 = -10.0000000000000
    x26 = -64.0000000000000
    x27 = 206.000000000000
    x28 = -40.0000000000000
    x29 = -14.0000000000000
    x30 = -92.0000000000000
    x31 = -56.0000000000000
    x32 = 616.000000000000
    x33 = 40.0000000000000
    x34 = -8.00000000000000
    x35 = 46.0000000000000
    x36 = 532.000000000000
    x37 = 22.0000000000000
    x38 = 58.0000000000000
    x39 = 26.0000000000000
    x40 = 76.0000000000000
    x41 = 28.0000000000000
    x42 = 74.0000000000000
    x43 = 650.000000000000
    x44 = 8.00000000000000
    x45 = -52.0000000000000
    x46 = -38.0000000000000
    x47 = 100.000000000000
    x48 = -44.0000000000000
    x49 = -68.0000000000000
    x50 = -4.00000000000000
    x51 = 62.0000000000000
    x52 = 640.000000000000
    x53 = 578.000000000000
    x54 = 82.0000000000000
    x55 = -86.0000000000000
    x56 = -76.0000000000000
    x57 = -22.0000000000000
    x58 = -34.0000000000000
    x59 = 98.0000000000000
    x60 = -62.0000000000000
    x61 = 38.0000000000000
    x62 = 50.0000000000000
    x63 = 20.0000000000000
    x64 = 64.0000000000000
    x65 = 56.0000000000000
    x66 = 68.0000000000000
    x67 = 14.0000000000000
    x68 = -26.0000000000000
    x69 = -2.00000000000000
    x70 = 88.0000000000000
    x71 = 10.0000000000000
    x72 = 86.0000000000000
    x73 = -94.0000000000000
    x74 = -20.0000000000000
    x75 = -70.0000000000000
    x76 = -98.0000000000000
    x77 = 44.0000000000000
    x78 = -74.0000000000000
    x79 = -16.0000000000000
    x80 = -80.0000000000000