sin(pi*sin(x))=-1 (уравнение)

Уравнение с неизвестным  :

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

    Решение

    Вы ввели [src]
    sin(pi*sin(x)) = -1
    $$\sin{\left (\pi \sin{\left (x \right )} \right )} = -1$$
    Подробное решение
    Дано уравнение
    $$\sin{\left (\pi \sin{\left (x \right )} \right )} = -1$$
    преобразуем
    $$\sin{\left (\pi \sin{\left (x \right )} \right )} + 1 = 0$$
    $$\sin{\left (\pi \sin{\left (x \right )} \right )} + 1 = 0$$
    Сделаем замену
    $$w = \sin{\left (\pi \sin{\left (x \right )} \right )}$$
    Переносим свободные слагаемые (без w)
    из левой части в правую, получим:
    $$w = -1$$
    Получим ответ: w = -1
    делаем обратную замену
    $$\sin{\left (\pi \sin{\left (x \right )} \right )} = w$$
    подставляем w:
    График
    Быстрый ответ [src]
         -pi 
    x1 = ----
          6  
    $$x_{1} = - \frac{\pi}{6}$$
         7*pi
    x2 = ----
          6  
    $$x_{2} = \frac{7 \pi}{6}$$
    x3 = pi - re(asin(3/2)) - I*im(asin(3/2))
    $$x_{3} = - \Re{\left(\operatorname{asin}{\left (\frac{3}{2} \right )}\right)} + \pi - i \Im{\left(\operatorname{asin}{\left (\frac{3}{2} \right )}\right)}$$
    x4 = I*im(asin(3/2)) + re(asin(3/2))
    $$x_{4} = \Re{\left(\operatorname{asin}{\left (\frac{3}{2} \right )}\right)} + i \Im{\left(\operatorname{asin}{\left (\frac{3}{2} \right )}\right)}$$
    Численный ответ [src]
    x1 = -31.9395254382000
    x2 = 12.0427717676000
    x3 = -59.1666617677000
    x4 = -13.0899690527000
    x5 = 16.2315620577000
    x6 = 56.0250689535000
    x7 = 28.7979324994000
    x8 = -46.6002912131000
    x9 = -44.5058957425000
    x10 = -63.3554519472000
    x11 = -27.7507351062000
    x12 = -82.2050076241000
    x13 = 41.3643028836000
    x14 = 97.9129711005000
    x15 = -2.61799415622000
    x16 = -90.5825882918000
    x17 = -78.0162175295000
    x18 = -15.1843646363000
    x19 = -40.3171056108000
    x20 = 18.3259571008000
    x21 = 93.7241810058000
    x22 = -78.0162175469000
    x23 = -34.0339203818000
    x24 = -71.7330322692000
    x25 = 74.8746252322000
    x26 = -19.3731547999000
    x27 = -71.7330324565000
    x28 = 91.6297858356000
    x29 = 87.4409956755000
    x30 = -65.4498471137000
    x31 = 30.8923281906000
    x32 = -6.80678371243000
    x33 = 79.0634151747000
    x34 = 47.6474886876000
    x35 = 100.007366130000
    x36 = -132.470489694000
    x37 = -21.4675499569000
    x38 = 72.7802296386000
    x39 = -0.523598600500000
    x40 = 53.9306739413000
    x41 = -38.2227104658000
    x42 = 24.6091423485000
    x43 = 43.4586985390000
    x44 = 85.3466004511000
    x45 = 49.7418838492000
    x46 = 66.4970443582000
    x47 = -25.6563400576000
    x48 = -69.6386372153000
    x49 = 816648.109122000
    x50 = -84.2994027610000
    x51 = 68.5914394978000
    x52 = 5.75958669198000
    x53 = 9.94837678071000
    x54 = 22.5147472004000
    x55 = -1133.59134885000
    x56 = 3.66519153871000
    x57 = -88.4881928865000
    x58 = 85.3465999674000
    x59 = 62.3082542600000
    x60 = 60.2138592228000
    x61 = -75.9218226842000
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