已知sin(x+4/派)=三分之一,求sinx

已知sin(x+4/派)=三分之一,求sinx
已知sin(x+4/派)=三分之一,求sinx

已知sin(x+4/派)=三分之一,求sinx
sin(x+π/4)=1/3,cos(x+π/4)=±√[1-cos²‎(x+π/4)]=±2√2/3,
sinx=sin[(x+π/4)-π/4]=sin(x+π/4)cos(π/4)-cos(x+π/4)sin(π/4)=(√2/2)[sin(x+π/4)-cos(x+π/4)],
当cos(x+π/4)=2√2/3时,sinx=(√2/2)[(2√2/3-1/3)=(4-√2)/6,
当cos(x+π/4)=-2√2/3时,sinx=(√2/2)[(-2√2/3-1/3)=-(4+√2)/6,