求sinx=(1\3),2π<x<3π,那么sin(x\2) + cos(x\2)
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![求sinx=(1\3),2π<x<3π,那么sin(x\2) + cos(x\2)](/uploads/image/z/1618716-12-6.jpg?t=%E6%B1%82sinx%3D%EF%BC%881%5C3%EF%BC%89%2C2%CF%80%EF%BC%9Cx%EF%BC%9C3%CF%80%2C%E9%82%A3%E4%B9%88sin%EF%BC%88x%5C2%EF%BC%89+%EF%BC%8B+cos%EF%BC%88x%5C2%29)
求sinx=(1\3),2π<x<3π,那么sin(x\2) + cos(x\2)
求sinx=(1\3),2π<x<3π,那么sin(x\2) + cos(x\2)
求sinx=(1\3),2π<x<3π,那么sin(x\2) + cos(x\2)
2π<x<3π π<x/2<3π/3 sin(x\2) + cos(x\2)
∵2π<x<3π
∴ π<x/2<3π/3
∴ sin(x\2) + cos(x\2)<0
∴[sin(x\2) + cos(x\2) ]²=1+sinx=4/3
∴sin(x\2) + cos(x\2) =-2√3/3
因为[sin(x\2) + cos(x\2)]²=1+sinx=1+1/3=4/3
又因为,2π<x<3π
所以,π<x/2<3π/2 即,x/2是第三象限的角,
所以,sin(x/2)<0, cos(x/2)<0
所以,sin(x/2)+cos(x/2)=-2√3/3