已知sinα=2/3,α∈(π/2,π),求cos(π/3+α),cos(π/3-α)
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已知sinα=2/3,α∈(π/2,π),求cos(π/3+α),cos(π/3-α)
已知sinα=2/3,α∈(π/2,π),求cos(π/3+α),cos(π/3-α)
已知sinα=2/3,α∈(π/2,π),求cos(π/3+α),cos(π/3-α)
sinα=2/3,α∈(π/2,π),
∴cosα=-(1-sin²α)½=-√5/3
∴cos(π/3+α)=cosπ/3·cosα-sinπ/3·sinα=1/2·(-√5/3)-√3/2·2/3=-(√5+2√3)/6
cos(π/3-α)=cosπ/3·cosα+sinπ/3·sinα=1/2·(-√5/3)+√3/2·2/3=(2√3-√5)/6