Question

已知cosα=2/3，270度＜α＜360度，求tan(α-π/4)的值

我一遇到sin cos tan 就 迷糊.. o(T_T)o```怎么办啊

Answer 1

去看看

Answer 2

sinα=sqrt(5)/3
tan(α-π/4)
=(tanα-1)/(1+tanα)
=(sinα-cosα)/(sinα+cosα)
=(sqrt(5)-2)/(sqrt(5)+2)
=9-4sqrt(5)

Answer 3

270<a<360
所以sina<0
(sina)^2+(cosa)^2=1
cosa=2/3
所以 sina=-√5/3
tana=sina/cosa=-√5/2

tanπ/4=1
tam(a-π/4)
=(tana-tanπ/4)/(1+tana*tanπ/4)
=(-√5/2-1)/(1-√5/2)
=(√5+2)/(√5-2)
=9+4√5