Господин Экзамен
Другие калькуляторы
-
Как пользоваться?
- Уравнение:
- Уравнение 12/x+10=13
- Уравнение x^2-12x+20=0
- Уравнение (6x-12)(0,5x-4)=0
- Уравнение 500+(х+140)=2056
- Выразите {x} через y в уравнении:
- -11*x-4*y=11
- -17*x-2*y=-9
- -20*x-17*y=-11
- -11*x+16*y=-8
- Производная:
-
sin(sin(sin(x)))
- 1/2
- График функции y =:
- 1/2
- Предел функции:
- 1/2
-
Идентичные выражения
- sin(sin(sin(x)))= один / два
- синус от ( синус от ( синус от (x))) равно 1 делить на 2
- синус от ( синус от ( синус от (x))) равно один делить на два
- sinsinsinx=1/2
- sin(sin(sin(x)))=1 разделить на 2
-
Похожие выражения
- sin(sin(sinx))=1/2
sin(sin(sin(x)))=1/2 уравнение
С верным решением ты станешь самым любимым в группе❤️😊
Решение
Вы ввели
[src]
sin(sin(sin(x))) = 1/2
$$\sin{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)} = \frac{1}{2}$$
Подробное решение
Дано уравнение
$$\sin{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)} = \frac{1}{2}$$
преобразуем
$$\sin{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)} - \frac{1}{2} = 0$$
$$\sin{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)} - \frac{1}{2} = 0$$
Сделаем замену
$$w = \sin{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)}$$
Переносим свободные слагаемые (без w)
из левой части в правую, получим:
$$w = \frac{1}{2}$$
Получим ответ: w = 1/2
делаем обратную замену
$$\sin{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)} = w$$
подставляем w:
$$\sin{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)} = \frac{1}{2}$$
преобразуем
$$\sin{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)} - \frac{1}{2} = 0$$
$$\sin{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)} - \frac{1}{2} = 0$$
Сделаем замену
$$w = \sin{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)}$$
Переносим свободные слагаемые (без w)
из левой части в правую, получим:
$$w = \frac{1}{2}$$
Получим ответ: w = 1/2
делаем обратную замену
$$\sin{\left(\sin{\left(\sin{\left(x \right)} \right)} \right)} = w$$
подставляем w:
Сумма и произведение корней
[src]
сумма
/ /pi\\ / /pi\\ / / /pi\\\ / / /pi\\\ / / /5*pi\\\ / / /5*pi\\\ / / /5*pi\\\ / / /5*pi\\\ / / /pi\\\ / / /pi\\\ / / /5*pi\\\ / / /5*pi\\\ / / /5*pi\\\ / / /5*pi\\\
pi - asin|asin|--|| + asin|asin|--|| + pi - re|asin|pi - asin|--||| - I*im|asin|pi - asin|--||| + pi - re|asin|pi - asin|----||| - I*im|asin|pi - asin|----||| + pi - re|asin|asin|----||| - I*im|asin|asin|----||| + I*im|asin|pi - asin|--||| + re|asin|pi - asin|--||| + I*im|asin|pi - asin|----||| + re|asin|pi - asin|----||| + I*im|asin|asin|----||| + re|asin|asin|----|||
\ \6 // \ \6 // \ \ \6 /// \ \ \6 /// \ \ \ 6 /// \ \ \ 6 /// \ \ \ 6 /// \ \ \ 6 /// \ \ \6 /// \ \ \6 /// \ \ \ 6 /// \ \ \ 6 /// \ \ \ 6 /// \ \ \ 6 ///
$$\left(- \operatorname{asin}{\left(\operatorname{asin}{\left(\frac{\pi}{6} \right)} \right)} + \pi\right) + \left(\operatorname{asin}{\left(\operatorname{asin}{\left(\frac{\pi}{6} \right)} \right)}\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(- \operatorname{asin}{\left(\frac{\pi}{6} \right)} + \pi \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(- \operatorname{asin}{\left(\frac{\pi}{6} \right)} + \pi \right)}\right)}\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(\pi - \operatorname{asin}{\left(\frac{5 \pi}{6} \right)} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\pi - \operatorname{asin}{\left(\frac{5 \pi}{6} \right)} \right)}\right)}\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(\operatorname{asin}{\left(\frac{5 \pi}{6} \right)} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\operatorname{asin}{\left(\frac{5 \pi}{6} \right)} \right)}\right)}\right) + \left(\operatorname{re}{\left(\operatorname{asin}{\left(- \operatorname{asin}{\left(\frac{\pi}{6} \right)} + \pi \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(- \operatorname{asin}{\left(\frac{\pi}{6} \right)} + \pi \right)}\right)}\right) + \left(\operatorname{re}{\left(\operatorname{asin}{\left(\pi - \operatorname{asin}{\left(\frac{5 \pi}{6} \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\pi - \operatorname{asin}{\left(\frac{5 \pi}{6} \right)} \right)}\right)}\right) + \left(\operatorname{re}{\left(\operatorname{asin}{\left(\operatorname{asin}{\left(\frac{5 \pi}{6} \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\operatorname{asin}{\left(\frac{5 \pi}{6} \right)} \right)}\right)}\right)$$
=
4*pi
$$4 \pi$$
произведение
/ /pi\\ / /pi\\ / / /pi\\\ / / /pi\\\ / / /5*pi\\\ / / /5*pi\\\ / / /5*pi\\\ / / /5*pi\\\ / / /pi\\\ / / /pi\\\ / / /5*pi\\\ / / /5*pi\\\ / / /5*pi\\\ / / /5*pi\\\
pi - asin|asin|--|| * asin|asin|--|| * pi - re|asin|pi - asin|--||| - I*im|asin|pi - asin|--||| * pi - re|asin|pi - asin|----||| - I*im|asin|pi - asin|----||| * pi - re|asin|asin|----||| - I*im|asin|asin|----||| * I*im|asin|pi - asin|--||| + re|asin|pi - asin|--||| * I*im|asin|pi - asin|----||| + re|asin|pi - asin|----||| * I*im|asin|asin|----||| + re|asin|asin|----|||
\ \6 // \ \6 // \ \ \6 /// \ \ \6 /// \ \ \ 6 /// \ \ \ 6 /// \ \ \ 6 /// \ \ \ 6 /// \ \ \6 /// \ \ \6 /// \ \ \ 6 /// \ \ \ 6 /// \ \ \ 6 /// \ \ \ 6 ///
$$\left(- \operatorname{asin}{\left(\operatorname{asin}{\left(\frac{\pi}{6} \right)} \right)} + \pi\right) * \left(\operatorname{asin}{\left(\operatorname{asin}{\left(\frac{\pi}{6} \right)} \right)}\right) * \left(- \operatorname{re}{\left(\operatorname{asin}{\left(- \operatorname{asin}{\left(\frac{\pi}{6} \right)} + \pi \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(- \operatorname{asin}{\left(\frac{\pi}{6} \right)} + \pi \right)}\right)}\right) * \left(- \operatorname{re}{\left(\operatorname{asin}{\left(\pi - \operatorname{asin}{\left(\frac{5 \pi}{6} \right)} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\pi - \operatorname{asin}{\left(\frac{5 \pi}{6} \right)} \right)}\right)}\right) * \left(- \operatorname{re}{\left(\operatorname{asin}{\left(\operatorname{asin}{\left(\frac{5 \pi}{6} \right)} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\operatorname{asin}{\left(\frac{5 \pi}{6} \right)} \right)}\right)}\right) * \left(\operatorname{re}{\left(\operatorname{asin}{\left(- \operatorname{asin}{\left(\frac{\pi}{6} \right)} + \pi \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(- \operatorname{asin}{\left(\frac{\pi}{6} \right)} + \pi \right)}\right)}\right) * \left(\operatorname{re}{\left(\operatorname{asin}{\left(\pi - \operatorname{asin}{\left(\frac{5 \pi}{6} \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\pi - \operatorname{asin}{\left(\frac{5 \pi}{6} \right)} \right)}\right)}\right) * \left(\operatorname{re}{\left(\operatorname{asin}{\left(\operatorname{asin}{\left(\frac{5 \pi}{6} \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\operatorname{asin}{\left(\frac{5 \pi}{6} \right)} \right)}\right)}\right)$$
=
/ / /pi\\\ / / / /pi\\\ / / /pi\\\\ / / / /5*pi\\\ / / /5*pi\\\\ / / / /5*pi\\\ / / /5*pi\\\\ / / / /pi\\\ / / /pi\\\\ / / / /5*pi\\\ / / /5*pi\\\\ / / / /5*pi\\\ / / /5*pi\\\\ / /pi\\ -|pi - asin|asin|--|||*|I*im|asin|pi - asin|--||| + re|asin|pi - asin|--||||*|I*im|asin|pi - asin|----||| + re|asin|pi - asin|----||||*|I*im|asin|asin|----||| + re|asin|asin|----||||*|-pi + I*im|asin|pi - asin|--||| + re|asin|pi - asin|--||||*|-pi + I*im|asin|pi - asin|----||| + re|asin|pi - asin|----||||*|-pi + I*im|asin|asin|----||| + re|asin|asin|----||||*asin|asin|--|| \ \ \6 /// \ \ \ \6 /// \ \ \6 //// \ \ \ \ 6 /// \ \ \ 6 //// \ \ \ \ 6 /// \ \ \ 6 //// \ \ \ \6 /// \ \ \6 //// \ \ \ \ 6 /// \ \ \ 6 //// \ \ \ \ 6 /// \ \ \ 6 //// \ \6 //
$$- \left(- \operatorname{asin}{\left(\operatorname{asin}{\left(\frac{\pi}{6} \right)} \right)} + \pi\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(- \operatorname{asin}{\left(\frac{\pi}{6} \right)} + \pi \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(- \operatorname{asin}{\left(\frac{\pi}{6} \right)} + \pi \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(\pi - \operatorname{asin}{\left(\frac{5 \pi}{6} \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\pi - \operatorname{asin}{\left(\frac{5 \pi}{6} \right)} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(\operatorname{asin}{\left(\frac{5 \pi}{6} \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\operatorname{asin}{\left(\frac{5 \pi}{6} \right)} \right)}\right)}\right) \left(- \pi + \operatorname{re}{\left(\operatorname{asin}{\left(- \operatorname{asin}{\left(\frac{\pi}{6} \right)} + \pi \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(- \operatorname{asin}{\left(\frac{\pi}{6} \right)} + \pi \right)}\right)}\right) \left(- \pi + \operatorname{re}{\left(\operatorname{asin}{\left(\pi - \operatorname{asin}{\left(\frac{5 \pi}{6} \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\pi - \operatorname{asin}{\left(\frac{5 \pi}{6} \right)} \right)}\right)}\right) \left(- \pi + \operatorname{re}{\left(\operatorname{asin}{\left(\operatorname{asin}{\left(\frac{5 \pi}{6} \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\operatorname{asin}{\left(\frac{5 \pi}{6} \right)} \right)}\right)}\right) \operatorname{asin}{\left(\operatorname{asin}{\left(\frac{\pi}{6} \right)} \right)}$$
Быстрый ответ
[src]
/ /pi\\
x_1 = pi - asin|asin|--||
\ \6 //
$$x_{1} = - \operatorname{asin}{\left(\operatorname{asin}{\left(\frac{\pi}{6} \right)} \right)} + \pi$$
/ /pi\\
x_2 = asin|asin|--||
\ \6 //
$$x_{2} = \operatorname{asin}{\left(\operatorname{asin}{\left(\frac{\pi}{6} \right)} \right)}$$
/ / /pi\\\ / / /pi\\\
x_3 = pi - re|asin|pi - asin|--||| - I*im|asin|pi - asin|--|||
\ \ \6 /// \ \ \6 ///
$$x_{3} = - \operatorname{re}{\left(\operatorname{asin}{\left(- \operatorname{asin}{\left(\frac{\pi}{6} \right)} + \pi \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(- \operatorname{asin}{\left(\frac{\pi}{6} \right)} + \pi \right)}\right)}$$
/ / /5*pi\\\ / / /5*pi\\\
x_4 = pi - re|asin|pi - asin|----||| - I*im|asin|pi - asin|----|||
\ \ \ 6 /// \ \ \ 6 ///
$$x_{4} = - \operatorname{re}{\left(\operatorname{asin}{\left(\pi - \operatorname{asin}{\left(\frac{5 \pi}{6} \right)} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\pi - \operatorname{asin}{\left(\frac{5 \pi}{6} \right)} \right)}\right)}$$
/ / /5*pi\\\ / / /5*pi\\\
x_5 = pi - re|asin|asin|----||| - I*im|asin|asin|----|||
\ \ \ 6 /// \ \ \ 6 ///
$$x_{5} = - \operatorname{re}{\left(\operatorname{asin}{\left(\operatorname{asin}{\left(\frac{5 \pi}{6} \right)} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\operatorname{asin}{\left(\frac{5 \pi}{6} \right)} \right)}\right)}$$
/ / /pi\\\ / / /pi\\\
x_6 = I*im|asin|pi - asin|--||| + re|asin|pi - asin|--|||
\ \ \6 /// \ \ \6 ///
$$x_{6} = \operatorname{re}{\left(\operatorname{asin}{\left(- \operatorname{asin}{\left(\frac{\pi}{6} \right)} + \pi \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(- \operatorname{asin}{\left(\frac{\pi}{6} \right)} + \pi \right)}\right)}$$
/ / /5*pi\\\ / / /5*pi\\\
x_7 = I*im|asin|pi - asin|----||| + re|asin|pi - asin|----|||
\ \ \ 6 /// \ \ \ 6 ///
$$x_{7} = \operatorname{re}{\left(\operatorname{asin}{\left(\pi - \operatorname{asin}{\left(\frac{5 \pi}{6} \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\pi - \operatorname{asin}{\left(\frac{5 \pi}{6} \right)} \right)}\right)}$$
/ / /5*pi\\\ / / /5*pi\\\
x_8 = I*im|asin|asin|----||| + re|asin|asin|----|||
\ \ \ 6 /// \ \ \ 6 ///
$$x_{8} = \operatorname{re}{\left(\operatorname{asin}{\left(\operatorname{asin}{\left(\frac{5 \pi}{6} \right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\operatorname{asin}{\left(\frac{5 \pi}{6} \right)} \right)}\right)}$$
Численный ответ
[src]
x1 = 2.55794718954594
x2 = -60.2739058822499
x3 = -24.5490957646745
x4 = -2988.23825902794
x5 = -79.1234618037887
x6 = 0.583645464043855
x7 = 46.540244339803
x8 = -198.503982640201
x9 = 88.5482397645581
x10 = 96.8057267972397
x11 = -81.0977635292908
x12 = -30.8322810718541
x13 = -87.3809488364704
x14 = 27778.545888505
x15 = -35.1411646535316
x16 = -18.2659104574949
x17 = 40.2570590326235
x18 = 57.1323132286601
x19 = -28.857979346352
x20 = 27.6906884182643
x21 = 44.565942614301
x22 = 75.9818691501989
x23 = -93.6641341436499
x24 = 71.6729855685214
x25 = 65.3898002613418
x26 = 25.7163866927622
x27 = -3.72523811763365
x28 = -53.9907205750703
x29 = -11.9827251503153
x30 = -10.0084234248132
x31 = 6.86683077122344
x32 = -43.3986516862132
x33 = 38.2827573071214
x34 = 101.114610378917
x35 = 63.4154985358397
x36 = 50.8491279214805
x37 = 6976.89363815889
x38 = -85.4066471109683
x39 = 90.5225414900601
x40 = 321.026096130203
x41 = 33.9738737254439
x42 = -16.2916087319928
x43 = -97.9730177253275
x44 = -72.8402764966091
x45 = -91.6898324181479
x46 = -49.6818369933928
x47 = 21.4075031110847
x48 = 84.2393561828806
x49 = -37.1154663790337
x50 = 8.84113249672552
x51 = -55.9650223005724
x52 = -74.8145782221112
x53 = 52.8234296469826
x54 = -66.5570911894295
x55 = 15.1243178039051
x56 = 314.742910823023
x57 = 59.1066149541622
x58 = 19.4332013855826
x59 = -99.9473194508295
x60 = -68.5313929149316
x61 = -62.248207607752
x62 = -47.7075352678908
x63 = 31.9995719999418
x64 = 77.956170875701
x65 = -22.5747940391724
x66 = 82.2650544573785
x67 = 69.6986838430193
x68 = -5.69953984313573
x69 = 94.8314250717377
x70 = 13.150016078403
x71 = -41.4243499607112
x71 = -41.4243499607112
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