已知cos(x+π/4)=3/5,π/2<x<3π/2,求sin(2x+π/4)的值

问题描述:

已知cos(x+π/4)=3/5,π/2<x<3π/2,求sin(2x+π/4)的值

sin(x+π/4)= -4/5
sinx + cosx = -4√2/5
sin2x = 7/25
cos2x = 24/25
sin(2x+π/4)=31√2/50

cos(x+π/4)=√2/2(cosx-sinx)=3/5 cosx-sinx=3√2/5(cosx-sinx)^2=(3√2/5)^2 1-2sinxcosx=18/25 sin2x=7/25 cos(x+π/4)=3/5,π/2<x<3π/2 x+π/4 位于第4象限 所以5π/2<2x<3πcos2x...