正余弦加权叠加式的研究

An Investigation into Sine and Cosine Weighted-repeated Formula

Acos(ωt) +Bsin(ωt) =Csin(ωt+D)中 ,令A =k1a、B =k2 b、C =k3 (A2 +B2 ) 1/2 =k3 (a2 +b2 ) 1/2 、D =k4 β ,并规定a、b、(A2 +B2 ) 1/2 和 β都取A、B、C、D的绝对值 ,即a >0、b >0、(A2 +B2 ) 1/2 >0、β≥ 0 ,推导出 :Acos(ωt) +Bsin(ωt) =F(B) (A2 +B2 ) 1/2 sin[ωt+F(AB) β]其中F(B) =B/ |B| ,F(AB) =AB/ |AB| ,β =tg- 1|A/B| ,(A2 +B2 ) 1/2 >0 .

In this paper, starting from formula A cos (ωt)+B sin (ωt)=C sin (ωt+D), through detailed calculation, the author finally gets the sine-cosine weighted formula: A cos (ωt)+B sin (ωt)=F(B)(A 2+B 2) 1/2 sin [ωt+F(AB)β], where F(B)=B/|B|,F(AB)=AB/|AB|,β =tg -1 |A/B|,(A 2+B 2) 1/2 >0.