已知cos(a+π/4)=3/5,π/2≤a≤3π/2,求cos(2a+3π/4)的值

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/23 11:16:30
已知cos(a+π/4)=3/5,π/2≤a≤3π/2,求cos(2a+3π/4)的值已知cos(a+π/4)=3/5,π/2≤a≤3π/2,求cos(2a+3π/4)的值已知cos(a+π/4)=3

已知cos(a+π/4)=3/5,π/2≤a≤3π/2,求cos(2a+3π/4)的值
已知cos(a+π/4)=3/5,π/2≤a≤3π/2,求cos(2a+3π/4)的值

已知cos(a+π/4)=3/5,π/2≤a≤3π/2,求cos(2a+3π/4)的值
因为cos(a+π/4)=3/5>0,
π/2

cos(a+π/4)=3/5 cos(2a+π/2)=2*(3/5)^2-1= -7/25 (II,III象限) sin(2a+π/2)=+/-24/25
cos(2a+3π/4)= cos(2a+π/2)cos(π/4)- sin(2a+π/2)sin(π/4)
=-7/25*根号2/2+/-24/25*根号2/2
-17根号2/50 -31根号2/50