(cosa+1)/(sina+3)=ma为[0°,180°]求m的取值范围

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(cosa+1)/(sina+3)=ma为[0°,180°]求m的取值范围
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(cosa+1)/(sina+3)=ma为[0°,180°]求m的取值范围
(cosa+1)/(sina+3)=m
a为[0°,180°]
求m的取值范围

(cosa+1)/(sina+3)=ma为[0°,180°]求m的取值范围
m=(sina+3-2)(sina+3)
=(sina+3)/(sina+3)-2/(sina+3)
=1-2/(sina+3)
0<=a<=180
0<=sina<=1
3<=sina+3<=4
所以1/4<=1/(sina+3)<=1/3
-2/3<=-2/(sina+3)<=-1/2
1-2/3<=1-2/(sina+3)<=1-1/2
所以1/3<=m<=1/2

y=cos²x+sinxcosx
=(1+cos2x)/2+1/2*sin2x
=(1/2)(sin2x+cos2x)+1/2
=(√2/2)(√2/2*sin2x+√2/2cos2x)+1/2
=(√2/2)(sin2xcosπ/4+cos2xsinπ/4)+1/2
=(√2/2)sin(2x+π/4)+1/2
T=2π/2=π