将f(x)=cos(x/4+π/3)sin(x/4-π/2)化成标准三角函数
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将f(x)=cos(x/4+π/3)sin(x/4-π/2)化成标准三角函数
![将f(x)=cos(x/4+π/3)sin(x/4-π/2)化成标准三角函数](/uploads/image/z/17339446-46-6.jpg?t=%E5%B0%86f%28x%29%3Dcos%28x%2F4%2B%CF%80%2F3%29sin%28x%2F4-%CF%80%2F2%29%E5%8C%96%E6%88%90%E6%A0%87%E5%87%86%E4%B8%89%E8%A7%92%E5%87%BD%E6%95%B0)
f(x)=cos(x/4+π/3)sin(x/4-π/2)
=-cos(x/4+π/3)cos(x/4)
=-[cos(x/4)cos(π/3)-sin(x/4)six(π/3)]cos(x/4) (拆分)
=-[1/2cos(x/4)-√3/2sin(x/4)]cos(x/4) (把cos乘进去)
=-[1/2cos(x/4)cos(x/4)-√3/2sin(x/4)cos(x/4)]
=-[1/4cos(x/2)+1/4-√3/4sin(x/2)]
=√3/4sin(x/2)-1/4cos(x/2)-1/4 (去负号)
=1/2[√3/2sin(x/2)-1/2cos(x/2)]-1/4
=1/2[cos(π/6)sin(x/2)-sin(π/6)cos(x/2)]-1/4
=1/2sin(x/2-π/6)-1/4
=-cos(x/4+π/3)cos(x/4)
=-[cos(x/4)cos(π/3)-sin(x/4)six(π/3)]cos(x/4) (拆分)
=-[1/2cos(x/4)-√3/2sin(x/4)]cos(x/4) (把cos乘进去)
=-[1/2cos(x/4)cos(x/4)-√3/2sin(x/4)cos(x/4)]
=-[1/4cos(x/2)+1/4-√3/4sin(x/2)]
=√3/4sin(x/2)-1/4cos(x/2)-1/4 (去负号)
=1/2[√3/2sin(x/2)-1/2cos(x/2)]-1/4
=1/2[cos(π/6)sin(x/2)-sin(π/6)cos(x/2)]-1/4
=1/2sin(x/2-π/6)-1/4
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