Question

已知cos(x-派/4)=根号2/10,x属于(派/2,3派/4)(1)求sinx的值.(2)求sin(2x+派/3).

Answer 1

cos(x-pai/4)=根号2/10x属于(派/2,3派/4)则（x-派/4）属于（派/4，派/2）(1)sinx=sin【(x-派/4)+派/4】=sin(x-派/4)cos派/4+cos(x-派/4)sin派/4 =根号2/2[sin(x-派/4)+cos(x-派/4)] cos(x-派/4)=根号2/10 所以sin (x-派/4 ）= 根号98/10 所以 原式=sinx=根号2/2[（根号2/10+根号98/10）=0.8 (2) sin(2x+派/3).=sin2xcos派/3+cos2xsin派/3 =1/2sin2x+根号3/2cos2xsinx=0.8 ,x属于(派/2,3派/4 所以cosx=--0.6sin2x=2sinxcosx=--0.96 cos2x=(cosx)^2-(sinx)^2=--0.28sin(2x+派/3)=1/2sin2x+根号3/2cos2x=1/2(--0.96)+根号3/2(--0.28)=--0.48-0.14根号3

Answer 2

sin(x-π/4)=√(1-cos�0�5(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=4/52∵x∈(π/2,3π/4)∴cosx=-√(1-sin�0�5x)=-3/5∴sin2x=2sinxcosx=-24/25cos2x=2cos�0�5x-1=-7/25sin(2x+π/3)=sin2xcosπ/3+cos2xsinπ/3=-(24+7√3)/50