Question

数学 高中函数问题

已知 sin（x+π/4）= - 3/5
则 sin 2x =

Answer 1

sin（x+π/4）=sinxcosπ/4+sinπ/4cosx=根号2/2[sinx+cosx]= - 3/5
[sinx+cosx]= - 3/5*根号2
[sinx+cosx]^2=1+2sinxcosx=1+sin2x= 18/25
sin2x=-7/25

Answer 2

sin(2x)=cos(π/2-2x)=cos(2x-π/2)=-cos(2x+π/2)=-[1-2(sin(x+π/2))^2]
=-[1-2*(-3/5)^2]=-7/25

Answer 3

已知 sin（x+π/4）= - 3/5
则 sin 2x =
sin（x+π/4）=sinxcosπ/4+sinπ/4cosx=根号2/2[sinx+cosx]= - 3/5
[ sinx+cosx]= - 3/5*根号2
[sinx+cosx]^2=1+2sinxcosx=1+sin2x= 18/25
则 sin 2x =-7/25