已知sin(a-π/4）=1/3,则cos(a+π/4）=?

已知sin(a-π/4）=1/3,则cos(a+π/4）=?
已知sin(a-π/4）=1/3,则cos(a+π/4）=?

已知sin(a-π/4）=1/3,则cos(a+π/4）=?
cos(a+π/4) = cos(π/2-(π/4-a)) = sin(π/4-a) = -sin(a-π/4) = -1/3

根据sinα=－sin（α＋1/2π）得到sin(a-π/4）=－sin(a-π/4＋1/2π）=－sin(a＋π/4）=1/3
则sin(a＋π/4）=－1/3
所以cos(a+π/4）=±√（1－sin(a＋π/4）²）=±2/3√2

cos(a+π/4) = cos(a-π/4+π/2)=-sin(a-π/4）=-1/3