已知y=3sin(x+20)+5sin(x+80)求最小值

解答：

y=3sin(x+20°)+5sin(x+80°）
=3sin(x+20°)+5sin(x+20°+60°）
=3sin(x+20°)+5*[sin(x+20°)*cos60°+cos(x+20°)*sin60°]
=3sin(x+20°)+2.5sin(x+20°)+2.5√3*cos(x+20°)
=5.5sin(x+20°)+2.5√3*cos(x+20°)
=5.5*[sin(x+20°)+(5√3/11)*cos(x+20°)]
=5.5*[sin(x+20°)+tga*cos(x+20°)]
=5.5*[sin(x+20°)*cosa+cos(x+20°)*sina]/cosa
=7*sin(x+a+20°)

y=3sin(x+20°)+5sin(x+80°）最小值=-7，此时：sin(x+a+20°)=-1

求导
即 3cos x+5cos x=0
得 x=π/2+kπ
所以此时取的最小值