Question

3. Вычислите tg (arcsin1:2)​

Answer 1

tg(arcsin(x)) = x / √(1 - x²)

У цьому випадку x = 1/2:

tg(arcsin(1/2)) = (1/2) / √(1 - (1/2)²)

tg(arcsin(1/2)) = (1/2) / √(1 - 1/4)

tg(arcsin(1/2)) = (1/2) / √(3/4)

tg(arcsin(1/2)) = (1/2) / (√3/2)

tg(arcsin(1/2)) = 1/√3

Отже, tg(arcsin(1/2)) = 1/√3.