若cos(θ/2)=3/5,sin(θ/2)= -4/5,则角θ的终边落在哪条直线上?

题目

若cos(θ/2)=3/5,sin(θ/2)= -4/5,则角θ的终边落在哪条直线上?

答案

sinθ/2=3/5>1/2
2kπ+π/6<θ/2<2kπ+5π/6
4kπ+π/3<θ<4kπ+5π/3
cosθ/2=-4/5<-√2/2
2kπ+3π/4<θ/2<2kπ+5π/4
4kπ+3π/2<θ<4kπ+5π/2
所以
4kπ+3π/2<θ<4kπ+5π/3
所以在第四象限