Question

ctg a=-7/24 , 450<a<540  , найдите cos a/2  1) 0,96
2) - 4/5
3) 0,6
4) - 0,6
5) 4/5

Answer 1

Решение
Ctg a= - 7/24 , 450<a<540
ctg²a + 1 = 1/sin²a
sin²a = 1 / (ctg²a + 1)
sin²a = 1 / [(-7/24)² + 1] = 1 / [(49/576) + 1] = 576 / 625
 sina = 24/25
cosx = - √(1 - sin²a) = - √(1 - 576/625) = - √49/625 = - 7/25
sin²(a/2) = (1 - cosa)/2 = (1 + 7/25)/2 = 32/(25*2) = 16/25
sin(a/2) = 4/5