已知y=3sin(x+20)+5sin(x+80)求最小值
来源:百度知道 编辑:UC知道 时间:2024/07/02 10:02:54
如题
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
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