叶帅故居:f1=sin(#t/3+#/4),f2=(根号3)sin(#t/3-#/4),求f1+f2=?

来源:百度文库 编辑:查人人中国名人网 时间:2024/05/04 20:44:36
要过程,在线等,最先给出正确过程的加分

#是表示圆周率pi吗?

f1 = sin(#t/3+#/4)
= 2(cos#/3 * sin(#t/3+#/4))

f2 = √3sin(#t/3-#/4)
= 2(sin#/3 * sin(#t/3-#/4))
= -2(sin#/3 * cos(#t/3+#/4))

f1+f2 = 2( cos#/3 * sin(#t/3+#/4) - sin#/3 * cos(#t/3+#/4) )
= 2sin(#t/3+#/4 - #/3)
= 2sin(#t/3-#/12)

易知sin(#t/3+#/4)=cos[#/2-(#t/3+#/4)]=cos(#/4-#t/3)
=cos(#t/3-#/4)
所以f1+f2=(根号3)sin(#t/3-#/4)+cos(#t/3-#/4)
=2sin(#t/3-#/4+#/6)=2sin(#t/3-#/12)