tan((pi/3)*(x-4))=sqrt(3) (уравнение)

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    Найду корень уравнения: tan((pi/3)*(x-4))=sqrt(3)

    Решение

    Вы ввели
    [LaTeX]
       /pi        \     ___
    tan|--*(x - 4)| = \/ 3 
       \3         /        
    $$\tan{\left (\frac{\pi}{3} \left(x - 4\right) \right )} = \sqrt{3}$$
    Подробное решение
    [LaTeX]
    Дано уравнение
    $$\tan{\left (\frac{\pi}{3} \left(x - 4\right) \right )} = \sqrt{3}$$
    преобразуем
    $$\tan{\left (\pi \left(\frac{x}{3} - \frac{4}{3}\right) \right )} - \sqrt{3} = 0$$
    $$\tan{\left (\pi \left(\frac{x}{3} - \frac{4}{3}\right) \right )} - \sqrt{3} = 0$$
    Сделаем замену
    $$w = \tan{\left (\pi \left(\frac{x}{3} - \frac{4}{3}\right) \right )}$$
    Раскрываем скобочки в левой части ур-ния
    w - sqrt3 = 0

    Разделим обе части ур-ния на (w - sqrt(3))/w
    w = 0 / ((w - sqrt(3))/w)

    Получим ответ: w = sqrt(3)
    делаем обратную замену
    $$\tan{\left (\pi \left(\frac{x}{3} - \frac{4}{3}\right) \right )} = w$$
    подставляем w:
    График
    [LaTeX]
    Быстрый ответ
    [LaTeX]
    x1 = -1
    $$x_{1} = -1$$
    Численный ответ
    [LaTeX]
    x1 = -37.0000000000000
    x2 = 32.0000000000000
    x3 = 92.0000000000000
    x4 = -19.0000000000000
    x5 = -79.0000000000000
    x6 = -46.0000000000000
    x7 = 29.0000000000000
    x8 = 80.0000000000000
    x9 = 20.0000000000000
    x10 = -10.0000000000000
    x11 = 2.00000000000000
    x12 = -13.0000000000000
    x13 = -31.0000000000000
    x14 = -82.0000000000000
    x15 = -94.0000000000000
    x16 = 47.0000000000000
    x17 = 53.0000000000000
    x18 = 5.00000000000000
    x19 = 95.0000000000000
    x20 = -40.0000000000000
    x21 = 68.0000000000000
    x22 = -61.0000000000000
    x23 = -67.0000000000000
    x24 = -100.000000000000
    x25 = -34.0000000000000
    x26 = -97.0000000000000
    x27 = -43.0000000000000
    x28 = 26.0000000000000
    x29 = 101.000000000000
    x30 = -28.0000000000000
    x31 = 89.0000000000000
    x32 = 38.0000000000000
    x33 = -49.0000000000000
    x34 = -88.0000000000000
    x35 = 8.00000000000000
    x36 = 41.0000000000000
    x37 = -16.0000000000000
    x38 = -73.0000000000000
    x39 = 71.0000000000000
    x40 = -22.0000000000000
    x41 = 23.0000000000000
    x42 = 62.0000000000000
    x43 = -4.00000000000000
    x44 = -91.0000000000000
    x45 = -76.0000000000000
    x46 = -7.00000000000000
    x47 = 98.0000000000000
    x48 = -64.0000000000000
    x49 = 74.0000000000000
    x50 = -55.0000000000000
    x51 = 50.0000000000000
    x52 = 83.0000000000000
    x53 = 56.0000000000000
    x54 = -25.0000000000000
    x55 = 14.0000000000000
    x56 = 59.0000000000000
    x57 = -1.00000000000000
    x58 = 77.0000000000000
    x59 = 86.0000000000000
    x60 = -58.0000000000000
    x61 = 35.0000000000000
    x62 = -70.0000000000000
    x63 = 44.0000000000000
    x64 = -52.0000000000000
    x65 = 17.0000000000000
    x66 = 65.0000000000000
    x67 = 11.0000000000000
    x68 = -85.0000000000000