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Обчислити sinα/2 , якщо sin α =5/13 і π/2< α < π.
Обчислити sinα/2 , якщо sin α =5/13 і π/2< α < π.
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Ответ:
cos^2 (a) + sin^2(a) = 1
cos^2(a) = 169/169 - 25/169 = 144/169
cos(a) = - 12/13 ( т. к. 3я четверть)
sin(2a) = 2sin(a) * cos(a) = 2 * 12/13 * 5/13 = 120/169