已知y=3sin(x+20)+5sin(x+80),求最大值?

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已知y=3sin(x+20)+5sin(x+80),求最大值?
已知y=3sin(x+20)+5sin(x+80),求最大值?

已知y=3sin(x+20)+5sin(x+80),求最大值?
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°)最大值=7,此时:sin(x+a+20°)=1