函数f(x)=根号3sinx-cosx=2sin(x-π/6)为么

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函数f(x)=根号3sinx-cosx=2sin(x-π/6)为么

函数f(x)=根号3sinx-cosx=2sin(x-π/6)为么
函数f(x)=根号3sinx-cosx=2sin(x-π/6)为么

函数f(x)=根号3sinx-cosx=2sin(x-π/6)为么
f(x)=√3sinx-cosx
=2sin(x-π/6)

f(x) =根号3 sinx - cosx = 2(根号3/2 sinx - 1/2 cosx) = 2(sinx cosπ/6 - cosx sinπ/6) = 2sin(x-π/6)

f(x)=2*(根号3/2*sinx-1/2*cosx)
根号3/2=cosπ/6
1/2=sinπ/6
f(x)
=2*(cosπ/6sinx-sinπ/6cosx)
后面括号里的是正弦的两角差公式
=2sin(x-π/6)