已知tanθ=34，θ为第三象限角，求cos(θ-π4)的值．

Question

已知tanθ=(3)/(4)，θ为第三象限角，求cos(θ-(π)/(4))的值．

Answer 1

∵tanθ=(3)/(4)，θ为第三象限角，sin²θ+cos²θ=1，∴cosθ=-(4)/(5)，sinθ=-(3)/(5)，
∴cos(θ-(π)/(4))=cosθcos(π)/(4)+sinθsin(π)/(4)=-(4)/(5)•(√(2))/(2)-(3)/(5)•(√(2))/(2)=-(7√(2))/(10)．