三角函数已知sin（a+(∏/4）=3/5,0.5∏

Question

三角函数
已知sin（a+(∏/4）=3/5,0.5∏

Answer 1

∵sin(a+π/4)=3/5＞0
又∵a∈[π/2,3π/2）
∴a+π/4在第二象限
∴cos(a+π/4)=-4/5
∵cos(2a+π/2)
=2cos(a+π/4)^2-1
=2*16/25-1=7/25
sin(2a+π/2)
=2sin(a+π/4)cos(a+π/4)
=2*3/5*(-4/5)
=-24/25
∴cos(2a+π/4)
=cos[(2a+π/2)-π/4]
=(7/25)(√2/2)+(-24/25)(√2/2)
=-17√2/50