求值:sin(1/2arcsin(-12/13))

Question

求值:sin(1/2arcsin(-12/13))

Answer 1

令arcsin(-12/13)=α∈（-π/2,0),α/2∈(-π/4,0)
∴sinα=-12/13,cosα=√(1-sin²α)=5/13
∴sin²(α/2)=(1-cosα)/2=(1-5/13)/2=4/13
∵sin(α/2)