Question

已知COS(x-π/4)=根号2/10,x属于(π/2,3π/4)。(1)求sinx的值。(2)求sin(2x+π/3)

要过程，最好用高一知识

Answer 1

1
sin(x-π/4)=√(1-cos²(x-π/4))=7√2/10
∴sinx=sin[(x-π/4)+π/4]
=sin(x-π/4)cosπ/4+cos(x-π/4)sinπ/4
=4/5
2
∵x∈(π/2,3π/4)
∴cosx=-√(1-sin²x)=-3/5
∴sin2x=2sinxcosx=-24/25
cos2x=2cos²x-1=-7/25
sin(2x+π/3)
=sin2xcosπ/3+cos2xsinπ/3
=-(24+7√3)/50

Answer 2

(1)x属于(π/2,3π/4),x-π/4就属于（π/4，π/2），sin(x-π/4)>0,所以sin(x-π/4)=10分之4倍根号6，所以sin x=sin[(x-π/4)+π/4]，再用公式就带出来了，公式为sin(x+y)=sinx乘以cosy+cosx乘以siny