已知sin(x+4/派)=三分之一,求sinx
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 00:02:13
![已知sin(x+4/派)=三分之一,求sinx](/uploads/image/z/10319041-1-1.jpg?t=%E5%B7%B2%E7%9F%A5sin%28x%2B4%2F%E6%B4%BE%29%3D%E4%B8%89%E5%88%86%E4%B9%8B%E4%B8%80%2C%E6%B1%82sinx)
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,