Дано: cos α = 1/4

Найдем синус α:
sin^2 α + cos^2 α = 1
sin^2 α + (1/4)^2 = 1
sin^2 α + 1/16 = 1
sin^2 α = 1 - 1/16
sin^2 α = 15/16
sin α = ±√(15/16) = ±√15 / 4

Находим тангенс α:
tg α = sin α / cos α
tg α = (±√15 / 4) / (1/4)
tg α = ±√15

Итак, sin α = ±√15 / 4, tg α = ±√15.