Question

sin(a+π/4）等于1/2 a∈（π/2，π） 求sin2a，cos2a的值 求过程 详细

Answer 1

由于sin(a＋π/4）＝1/2，则a＋π/4＝π/6＋2kπ或者5π/6＋2kπ 则a＝-π/12＋2kπ或者7π/12＋2kπ又由已知a的范围可以确定a＝7π/12。sin2a＝sin 7π/6＝-sinπ/6＝-1/2 cos2a＝cos7π/6＝-cosπ/6＝-√3/2 打字累的手疼，还有什么不懂的就问，谢谢:)

Answer 2

∵a∈(0.5π,π)
∴a+π/4∈(3π/4,5π/4)
又∵sin(a+π/4)=1/2
∴a+π/4∈(3π/4,π)
∴a∈(π,3π/4)
∴a+π/4=5π/6
∴a=7π/6
sin2a=sin7π/3=√3/2
cos2a=cos7π/3=1/2

Answer 3

a＋四分之派=2k派＋30或2k派＋150。
∵a属于二分之派到派。
∴a=105°
接下来应该没问题了吧。

Answer 4

sin(5π/6)=1/2
a=5π/6-π/4=7π/12
sin2a=sin7π/6=-sinπ/6=-1/2
cos2a=cos7π/6=-cosπ/6=-√3/2