Question

已知tanα=-3/4,π＜α＜2π,求cos(π/4-α)，sin(π/4+α）及tan(π/3-α)的值

已知tanα=-3/4,π＜α＜2π,求cos(π/4-α)，sin(π/4+α）及tan(π/3-α)的值

Answer 1

∵tanα=-3/4,π＜α＜2π,
∴当α在第二象限时，sina=3/5,cosa=-4/5
当α在第四象限时，sina=-3/5,cosa=4/5

cos(π/4-α)=cosπ/4cosa+sinπ/4sina=(根号2/2)(cosa+sina)=正负根2/10

sin(π/4+α）=sinπ/4cosa+cosπ/4sina=正负根
2/10

tan(π/3-α) =(tanπ/3-tana)/(1-tanπ/3tana)=(24-7倍根号3）/11