sin(sin(x))=0 (уравнение)

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    Найду корень уравнения: sin(sin(x))=0

    Решение

    Вы ввели [src]
    sin(sin(x)) = 0
    $$\sin{\left(\sin{\left(x \right)} \right)} = 0$$
    Подробное решение
    Дано уравнение
    $$\sin{\left(\sin{\left(x \right)} \right)} = 0$$
    преобразуем
    $$\sin{\left(\sin{\left(x \right)} \right)} - 1 = 0$$
    $$\sin{\left(\sin{\left(x \right)} \right)} - 1 = 0$$
    Сделаем замену
    $$w = \sin{\left(\sin{\left(x \right)} \right)}$$
    Переносим свободные слагаемые (без w)
    из левой части в правую, получим:
    $$w = 1$$
    Получим ответ: w = 1
    делаем обратную замену
    $$\sin{\left(\sin{\left(x \right)} \right)} = w$$
    подставляем w:
    График
    Быстрый ответ [src]
    x1 = 0
    $$x_{1} = 0$$
    x2 = pi
    $$x_{2} = \pi$$
    x3 = pi - re(asin(pi)) - I*im(asin(pi))
    $$x_{3} = - \operatorname{re}{\left(\operatorname{asin}{\left(\pi \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\pi \right)}\right)}$$
    x4 = I*im(asin(pi)) + re(asin(pi))
    $$x_{4} = \operatorname{re}{\left(\operatorname{asin}{\left(\pi \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\pi \right)}\right)}$$
    Численный ответ [src]
    x1 = -75.398223686155
    x2 = 34.5575191894877
    x3 = -84.8230016469244
    x4 = 28.2743338823081
    x5 = 2921.68116783851
    x6 = 9.42477796076938
    x7 = -15.707963267949
    x8 = 37.6991118430775
    x9 = 43.9822971502571
    x10 = -6.28318530717959
    x11 = 18.8495559215388
    x12 = 81.6814089933346
    x13 = -94.2477796076938
    x14 = 25.1327412287183
    x15 = -31.4159265358979
    x16 = -69.1150383789755
    x17 = -72.2566310325652
    x18 = -53.4070751110265
    x19 = 13540.264336972
    x20 = 84.8230016469244
    x21 = 6.28318530717959
    x22 = -50.2654824574367
    x23 = -56.5486677646163
    x24 = -131.946891450771
    x25 = 50.2654824574367
    x26 = 21.9911485751286
    x27 = -12.5663706143592
    x28 = -3.14159265358979
    x29 = -25.1327412287183
    x30 = 62.8318530717959
    x31 = 56.5486677646163
    x32 = 12.5663706143592
    x33 = 75.398223686155
    x34 = 3.14159265358979
    x35 = -97.3893722612836
    x36 = 0.0
    x37 = -37.6991118430775
    x38 = -100.530964914873
    x39 = -34.5575191894877
    x40 = -43.9822971502571
    x41 = -65.9734457253857
    x42 = 31.4159265358979
    x43 = -2667.21216289773
    x44 = -78.5398163397448
    x45 = -9.42477796076938
    x46 = 69.1150383789755
    x47 = 94.2477796076938
    x48 = 47.1238898038469
    x49 = -21.9911485751286
    x50 = -62.8318530717959
    x51 = 29666.0594278484
    x52 = 59.6902604182061
    x53 = 97.3893722612836
    x54 = 40.8407044966673
    x55 = -81.6814089933346
    x56 = -40.8407044966673
    x57 = 78.5398163397448
    x58 = -59.6902604182061
    x59 = -87.9645943005142
    x60 = -116.238928182822
    x61 = -91.106186954104
    x62 = -47.1238898038469
    x63 = 72.2566310325652
    x64 = -28.2743338823081
    x65 = 53.4070751110265
    x66 = -18.8495559215388
    x67 = 15.707963267949
    x68 = 87.9645943005142
    x69 = 109.955742875643
    x70 = 65.9734457253857
    x71 = 91.106186954104
    x72 = 100.530964914873
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