已知tan(3π/2+θ）等于根号3,求cos(θ+7π/2）的值

已知tan(3π/2+θ）等于根号3,求cos(θ+7π/2）的值
已知tan(3π/2+θ）等于根号3,求cos(θ+7π/2）的值

已知tan(3π/2+θ）等于根号3,求cos(θ+7π/2）的值
cos(θ+7π/2)=cos(θ+3π/2)
tan(θ+3π/2)=sin(θ+3π/2)/cos(θ+3π/2)=√3 sin(θ+3π/2)=√3cos(θ+3π/2)
sin²(θ+3π/2)+cos²(θ+3π/2)=1 -->cos²(θ+3π/2)=1/4
显然θ+3π/2在一三象限 故cos(θ+7π/2)=cos(θ+3π/2)=±1/2