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Консультация № 187609
06.11.2013, 00:38
81.30 руб.
0
4
2
Здравствуйте! У меня возникли сложности с таким вопросом: Вычислите: a). arccos(sin0,8п); б). arccos(cos3,5). Заранее благодарен.
Обсуждение
06.11.2013, 02:58
общий
это ответ
Здравствуйте, Тимофеев Алексей Валентинович!
, если 
. Так что
a)
.
б) 3.5 чуть больше
. Так что
.
, если . Так чтоa)
.б) 3.5 чуть больше
. Так что.
Неизвестный
06.11.2013, 03:26
общий
это ответ
Здравствуйте, Тимофеев Алексей Валентинович!
1. arccos(x)+arcsin(x) = п/2 <=> arccos(x) = п/2 - arcsin(x)
x = sin(0.8п)
0.8п > п/2, а функция arcsin отображается на интервал [-п/2;п/2]
sin(п-x) = sin(x)
sin(0.8п) = sin(п-0.2п) = sin(0.2п)
arcsin(sin(x)) = x, если x на интервале [-п/2;п/2]
arcsin(sin(0.8п)) = arcsin(sin(0.2п)) = 0.2п
Значит, arccos(sin(0.8п)) = п/2 - arcsin(sin(0.8п)) = п/2 - arcsin(sin(0.2п)) = 0.5п - 0.2п = 0.3п
2. arccos(cos(3.5))
arccos(cos(x)) = x, если x на интервале [0;п]
cos(x) = cos (2п-x)
cos (3.5) = cos (2п-3.5)
arccos(cos (2п-3.5)) = 2п-3.5
1. arccos(x)+arcsin(x) = п/2 <=> arccos(x) = п/2 - arcsin(x)
x = sin(0.8п)
0.8п > п/2, а функция arcsin отображается на интервал [-п/2;п/2]
sin(п-x) = sin(x)
sin(0.8п) = sin(п-0.2п) = sin(0.2п)
arcsin(sin(x)) = x, если x на интервале [-п/2;п/2]
arcsin(sin(0.8п)) = arcsin(sin(0.2п)) = 0.2п
Значит, arccos(sin(0.8п)) = п/2 - arcsin(sin(0.8п)) = п/2 - arcsin(sin(0.2п)) = 0.5п - 0.2п = 0.3п
2. arccos(cos(3.5))
arccos(cos(x)) = x, если x на интервале [0;п]
cos(x) = cos (2п-x)
cos (3.5) = cos (2п-3.5)
arccos(cos (2п-3.5)) = 2п-3.5
5
Форма ответа
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