Дано: sin a = 24/25

Найдем сначала cos a, используя тригонометрическое соотношение sin^2(a) + cos^2(a) = 1:
cos^2(a) = 1 - sin^2(a)
cos^2(a) = 1 - (24/25)^2
cos^2(a) = 1 - 576/625
cos^2(a) = 49/625
cos(a) = ±√(49/625)
cos(a) = ±7/25

Теперь найдем sin(a/2) и cos(a/2) с помощью формул половинного угла:
sin(a/2) = ±√((1 - cos(a))/2)
sin(a/2) = ±√((1 - 7/25)/2)
sin(a/2) = ±√(18/50)
sin(a/2) = ±3√2/5

cos(a/2) = ±√((1 + cos(a))/2)
cos(a/2) = ±√((1 + 7/25)/2)
cos(a/2) = ±√(32/50)
cos(a/2) = ±4√2/5

Итак, sin(a/2) = ±3√2/5 и cos(a/2) = ±4√2/5.