Question

已知α,β,γ∈(0,π/2),且sinα=1/3,tanβ=√2,cosγ=3/4,则α,β,γ的大小之比.

Answer 1

tanβ=√2 而β∈(0,π/2)所以sinβ=√6/3

cosγ=3/4而γ∈(0,π/2)所以sinγ=√7/4

因为sinα=1/3,sinβ=√6/3,sinγ=√7/4

√6/3＞√7/4＞1/3,α,β,γ∈(0,π/2)所以β＞γ＞α