sin(pi*sin(x))=-1 (уравнение)

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

Вы ввели

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:

Быстрый ответ

     -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

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