(cosa+1)/(sina+3)=m

题目

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

答案

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