Question

известно что ctg ( t - π ) = - 3/4 и π/2 < t< π найдите a) cos ( 3π /2 - t)

Answer 1

ctg(t - π) = ctgt = -0,75.

a) cos(3π/2 - t) = -sint.
ctg²t + 1 = 1/sin²t <=> sin²t = 1/(ctg²t + 1) = 0,64 => sint = 0,8, т.к. при π/2 < t < π sint > 0.
cos(3π/2 - t) = -sint = -0,8.

б) cos(π + t) = -cost.
cos²t = 1 - sin²t = 0,36 => cost = -0,6, т.к. при π/2 < t < π cost < 0.
cos(π + t) = -cost = 0,6.
Вроде так но проверь на всякий случай