已知sinα=1/3,α∈(π/2,π),求sin2α,cos2α,tan2α的值
问题描述:
已知sinα=1/3,α∈(π/2,π),求sin2α,cos2α,tan2α的值
答
α∈(π/2,π)
cosα = -√(1-1/9) = -2√2/3
sin2α = 2sinα * cosα = 1/3 * -2√2/3 = -2√2/9
cos2α = 2cos²α-1 = 2 * 8/9 - 1 = 7/9
tan2α = sin2α/cos2α = -2√2/7