Suppose 45° < 𝜃 < 90°, let 𝑎=log1/2(sin𝜃), b = log1/2(cos𝜃) ,𝑐 = log1/2(tan𝜃), 𝑑 = log1/2(sec𝜃). Order 𝑎, 𝑏, 𝑐, 𝑑 from the smallest to the largest.

Answer 1

since logx is an increasing function, logx < logy if x < y
so the logs are in the same order as the trig values:
cosθ, sinθ, tanθ, secθ
so, b,a,c,d

not sure what the 1/2 factor means; all it does is add log 1/2 to each value