a+b=120度,求y=sina+cosb的最小值
y=sina+cosb= sina+sin(90-b)=2sin((a+90-b)/2)cos((a+b-90)/2)
=2sin((a+90-b)/2)cos((120-90)/2)=2sin((a+90-b)/2)cos15
當(dāng)(a+90-b)/2=(a-b+90)/2=360K+270度,（K為任意整數(shù)）,即a-b=720K+450度時(shí),
sin((a+90-b)/2)=-1最小,此時(shí)由
由a+b=120度,a-b=720K+450度
解得a=360K+285度,b=-360K-115度
故當(dāng)a=360K+285度,b=-360K-115度時(shí),y=sina+cosb取最小值-cos15=-(√2+√6)/4.