√3sin(100πt+π/3)+sin(100πt-π/6)化简
问题描述:
√3sin(100πt+π/3)+sin(100πt-π/6)化简
答
因为 100πt+π/3= π/2+ (100πt-π/6)所以 sin(100πt+π/3)=sin[π/2 +(100πt -π/6)]=cos(100πt- π/6)所以 原式=√3cos(100πt-π/6)+sin(100πt-π/6)=2[(√3/2)·cos(100πt-π/6)+(1/2)·sin(100πt-π...为什么100πt+π/3= π/2+ (100πt-π/6)因为 π/3= π/2- π/6为什么2[(√3/2)·cos(100πt-π/6)+(1/2)·sin(100πt-π/6)]=2sin(100πt-π/6+π/3)(√3/2)·cos(100πt-π/6)+(1/2)·sin(100πt-π/6)=sin(π/3)·cos(100πt-π/6)+cos(π/3)·sin(100πt-π/6)=sin(100πt-π/6+π/3),这是两角和的正弦公式.