Question

已知cosx/8=-4/5,8派<x<12派，求sinx/4,cosx/4,tanx/4的值

Answer 1

8π<x<12π
π<x/8<3π/2
2π<x/4<3π
sin(x/4)>0
cos(x/4)=2cos²(x/8)-1=2×16/25-1=7/25
sin²(x/4)=1-cos²(x/4)=1-(7/25)²=24/25
sin(x/4)=2√6/5
tan(x/4)=sin(x/4)/cos(x/4)=(2√6/5)/(7/25)=10√6/7

Answer 2

sina=-24/25
cosa=-7/25
π<a<3π/2
π/2<a/2<3π/4
所以sin(a/2)>0,cos(a/2)<0,tan(a/2)<0
sin²(a/2)=(1-cosa)/2=16/25
sin(a/2)=4/5
cos²(a/2)=(1+cosa)/2=9/25
cos(a/2)=-3/5
tan(a/2)=sin(a/2)/cos(a/2)=-4/3