已知函数f(x)=2√3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π)
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/07/18 15:10:24
已知函数f(x)=2√3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π)
f(x)=2√3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π)
=√3sin(x+π/2)+sinx
这一步是怎么来的
f(x)=2√3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π)
=√3sin(x+π/2)+sinx
这一步是怎么来的
x)=2√3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π)
f(x)=根号3sin[2(x/2+π/4)]+sinx
f(x)=根号3sin(x+π/2)+sinx
再问: 不明白
再答: sin(2x)=2sinxcosx 这是公式 所以:2√3sin(x/2+π/4)cos(x/2+π/4) =根号3sin[2(x/2+π/4)] sin(x+π)=-sinx 也是公式 -sin(x+π)=-(-sinx)=sinx =√3sin(x+π/2)+sinx =-根号3cosx+sinx=2(-根号3/2cosx+1/2sinx) =2(cos5π/6cosx+sin5π/6sinx) =2cos(x-5π/6)
f(x)=根号3sin[2(x/2+π/4)]+sinx
f(x)=根号3sin(x+π/2)+sinx
再问: 不明白
再答: sin(2x)=2sinxcosx 这是公式 所以:2√3sin(x/2+π/4)cos(x/2+π/4) =根号3sin[2(x/2+π/4)] sin(x+π)=-sinx 也是公式 -sin(x+π)=-(-sinx)=sinx =√3sin(x+π/2)+sinx =-根号3cosx+sinx=2(-根号3/2cosx+1/2sinx) =2(cos5π/6cosx+sin5π/6sinx) =2cos(x-5π/6)
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