Задача 1. Вычислите sin β, tg β, ctg β, если cos β = 1/4.

Решение: 1. cos β = 1/4. 2. sin² β + cos² β = 1: sin² β = 1 - (1/4)² = 1 - 1/16 = 15/16, sin β = sqrt(15)/4. 3. tg β = sin β / cos β = (sqrt(15)/4) / (1/4) = sqrt(15). 4. ctg β = 1 / tg β = 1 / sqrt(15). Ответ: sin β = sqrt(15)/4, tg β = sqrt(15), ctg β = 1/sqrt(15).